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Mathematical assessment of the effect of traditional beliefs and customs on the transmission dynamics of the 2014 Ebola outbreaks

Mathematical assessment of the effect of traditional beliefs and customs on the transmission... Background: Ebola is one of the most virulent human viral diseases, with a case fatality ratio between 25% to 90%. The 2014 West African outbreaks are the largest and worst in history. There is no specific treatment or effective/safe vaccine against the disease. Hence, control efforts are restricted to basic public health preventive (non-pharmaceutical) measures. Such efforts are undermined by traditional/cultural belief systems and customs, characterized by general mistrust and skepticism against government efforts to combat the disease. This study assesses the roles of traditional customs and public healthcare systems on the disease spread. Methods: A mathematical model is designed and used to assess population-level impact of basic non-pharmaceutical control measures on the 2014 Ebola outbreaks. The model incorporates the effects of traditional belief systems and customs, along with disease transmission within health-care settings and by Ebola-deceased individuals. A sensitivity analysis is performed to determine model parameters that most affect disease transmission. The model is parameterized using data from Guinea, one of the three Ebola-stricken countries. Numerical simulations are performed and the parameters that drive disease transmission, with or without basic public health control measures, determined. Three effectiveness levels of such basic measures are considered. Results: The distribution of the basic reproduction number (R ) for Guinea (in the absence of basic control measures) is such that R ∈ [ 0.77, 1.35], for the case when the belief systems do not result in more unreported Ebola cases. When such systems inhibit control efforts, the distribution increases to R ∈ [ 1.15, 2.05]. The total Ebola cases are contributed by Ebola-deceased individuals (22%), symptomatic individuals in the early (33%) and latter (45%) infection stages. A significant reduction of new Ebola cases can be achieved by increasing health-care workers’ daily shifts from 8 to 24 hours, limiting hospital visitation to 1 hour and educating the populace to abandon detrimental traditional/cultural belief systems. Conclusions: The 2014 outbreaks are controllable using a moderately-effective basic public health intervention strategy alone. A much higher (> 50%) disease burden would have been recorded in the absence of such intervention. 2000 Mathematics Subject Classifications: 92B05, 93A30, 93C15. Keywords: Ebola, Community, Hospital, Health-care workers, Quarantine *Correspondence: agumel@asu.edu Simon A. Levin Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1904, USA School of Mathematical and Natural Sciences, Arizona State University, Phoenix, AZ 85069-7100, USA Full list of author information is available at the end of the article © 2015 Agusto et al.; licensee BioMed Central. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Agusto et al. BMC Medicine (2015) 13:96 Page 2 of 17 Background vessels, rendering the blood vessels to be more perme- Ebola virus disease (EVD), caused by Ebola virus (EBOV) able. The increased permeability causes the blood vessels and formerly known as Ebola hemorrhagic fever, is one to leak out blood [8]. The virus also evades the host’s nat- of the world’s most virulent diseases. The disease, which ural defense system, by infecting immune cells, a channel spreads in human and other mammalian populations, has through which it is transported to other body parts and a case fatality ratio from 25% to 90% in humans [1,2]. organs, such as the liver, spleen, kidney and brain [8]. The The first known case of EVD dates back to 1976, where virus can cause these organs to fail, leading to death of the two outbreaks occurred (in Sudan and in the Democratic infected human host. Republic of Congo, formerly Zaire; the later outbreak was Ebola-infected humans typically exhibit flu-like symp- identified near the Ebola River, where the disease got its toms during the initial phase of the infection [8], and can name [2,3]). Since then, other outbreaks have occurred, have, or progress to, other symptoms such as fever, severe most notably in parts of Central Africa [3]. However, the headache, muscle aches, weakness, vomiting, diarrhea, largest, and most devastating, outbreak of EVD is the 2014 stomach pains, loss of appetite and, at times, bleeding epidemic in three West African countries (Guinea, Liberia (which may be visible or internal) [8,10,11]. An infected and Sierra Leone). This EVD outbreak (believed to have human is infectious (i.e., capable of transmitting the dis- started in Guinea in March 2014 [2]) is the first to have ease to susceptible individuals) at the onset of symptoms occurred in West Africa [4]. [2,8]. Transmission typically occurs when a susceptible The disease, which also spread to Nigeria (started by an human comes into contact with virus-infected fluids, such airline passenger, who arrived from Liberia) and Senegal as blood, bodily secretions (e.g., feces, saliva, vomit, urine, (started by a student from Guinea, who arrived by land semen and sweat), organs or bodily fluids of an infected transportation) [2,4], spread to other regions outside human (dead or alive) [2,10]. Contact with such fluids Africa. For instance, some Ebola-infected patients were may be as a result of direct contact between suscepti- flown to the US, France, Germany, Norway, Spain and the ble and infected humans, or due to indirect contact with UK [5] for health-care delivery. The US diagnosed its first environments contaminated with the aforementioned flu- imported travel-related Ebola case in September 2014 (by ids [2]. Individuals with high risk of exposure to EBOV a person who had travelled to Dallas, Texas, from Liberia). are the immediate family members of Ebola-infected The imported case, who later died of the disease on 8 humans and health-care workers who treat Ebola-infected October 2014, resulted in the infection of two health-care patients. workers who cared for the deceased patient [6]. One of In the absence of a cure (a specific treatment) or effec- the cases flown to Spain also led to an infection of health- tive and safe vaccine against the spread of EBOV in care workers [5]. Additionally, a separate Ebola outbreak, humans, anti-Ebola control efforts are mostly restricted unrelated to the West African outbreaks, occurred in the to basic public health preventive measures, disease Democratic Republic of Congo [2]. By 15 October 2014, management and treatment of Ebola-related symptoms. the case count for the 2014 EVD was 8,997 with 4,493 Public health preventive measures include approved fatalities [6] (a case fatality ratio of about 50%). It should health-care techniques practiced by health-care workers be mentioned that these estimates include the cases for when dealing with Ebola-infected patients, or, in areas Nigeria, Senegal, Spain and the USA [7]. These num- around Ebola-infected patients, educating the public and bers increased to 15,935 and 5,689, respectively (36% case raising awareness of the disease, quarantine of suspected fatality ratio) by 23 November 2014. The latest update, cases, isolation of symptomatic cases, rapid laboratory dated 21 January 2015, shows a case count of 21,724 diagnostic tests, minimizing contact with bodily fluids, and 8,641 fatalities (representing a case fatality ratio of wearing protective equipment by health-care providers 40%) [7]. and proper handling of individuals who died of the Ebola The natural reservoir and host of the EBOV is consid- virus [2,10]. The disease management component of the ered (albeit not yet proven [4]) to be fruit bats of the control strategy (for infected patients) typically entails the Pteropodidae family [2]. It is hypothesized that the virus administration of intravenous fluids and balancing elec- is introduced into the human population when a human trolytes to hydrate the patient, the maintenance of oxygen comes into contact with the blood, organ secretions or levels and blood pressure, and possibly a transfusion with bodily fluids of an animal infected with the EBOV. The blood from a matching Ebola survivor [4]. incubation period of EBOV is between 2 and 21 days Recovery from the disease is possible (but the rate of [2,8,9] (although some studies have estimated the most recovery tends to be lower than that of the Ebola-induced common incubation period to be 8 to 10 days [10]). Dur- death rate [11]). Note that some experimental drugs (such ing the incubation period, the virus infects body cells, as ZMapp [12] and TKM Ebola [13]) and vaccines are replicates and bursts out of the infected cells, produc- being developed for use in humans (in fact, ZMapp was ing EBOV glycoproteins that attach to the inside of blood reportedly used to treat the two American volunteers Agusto et al. BMC Medicine (2015) 13:96 Page 3 of 17 who contracted the disease while in missionary service in in [9,16,17,19,20] did not account for disease spread by Liberia, although its safety and efficacy have not yet been Ebola-infected deceased individuals (prior to, or during, tested on humans [14]). However, a person’s best chances their burial or cremation), a feature that is known to play of survival, following the acquisition of the infection, is a major role in the current outbreaks [2]. Legrand et al. early diagnosis (and prompt and effective disease man- [18] developed a compartmental model, using data from agement). This is challenging, however, since the early the 1995 Democratic Republic of Congo and 2000 Uganda symptoms of Ebola are similar to those of some other dis- Ebola epidemic outbreaks. The model allowed for EBOV eases, such as malaria and typhoid fever (diseases that are transmission by infected humans in both the community endemic in the region ravaged by the 2014 EBOV out- and the hospital. breaks [10]). However, using approved laboratory tests, a Another important feature that plays a critical role in the definitive diagnosis of EBOV can be made [2]. It is known 2014 EVD outbreaks is traditional/cultural belief systems that Ebola infection confers permanent natural immu- and customs. For instance, while some individuals in the nity (in individuals who have recovered from the disease) three Ebola-stricken nations believe that there is no Ebola against re-infection [15]. Although a human may be clini- [23-25], others claim that it is government propaganda to cally cleared of the virus (i.e., is declared to be recovered), attract more foreign aid dollars [26], control the popu- a male may, however, still have the virus in his semen for 2 lation or harvest human organs [27]. Furthermore, some to 3 months [2,15], and it may be found in the breast milk susceptible members of the public (including those at high of breast-feeding mothers [15]. risk of EBOV infection) refuse to be quarantined because A number of mathematical models and statistical meth- of their belief, or fear, that they might be deliberately odshavebeenusedinanattempt to understand the infected during quarantine [27,28]. There is also a fear that transmission dynamics of EVD (see for instance [9,16-20], they will notbeabletogivealovedone whodiedofEbola and some of the references therein). In [9], a compart- a proper traditional burial (since Ebola-infected humans mental mathematical model was used to estimate the who die in hospitals are typically cremated [26,27,29], number of secondary cases generated by an index case a practice that is not accepted by those who harbor a (the basic reproduction number), in the absence or pres- belief in traditional burial rituals). Adherence to these ence of control measures, for the 1995 Congo and 2000 traditional/cultural beliefs and customs often leads some Uganda Ebola outbreaks. The study further highlighted family members to hide Ebola-infected loved ones (to the importance of basic public health control measures, evade the health-care system), resulting in the develop- such as public health education, contact tracing and quar- ment of shadow zones [28], where paramedics cannot antine of suspected cases, and the role such measures visit, and, invariably, resulting in significant underreport- can play in reducing the final size of the epidemics. Most ing of EVD cases [21,30] (the Centers for Disease Control recently, the basic reproduction number for the 2014 estimated a potential underreporting correction factor of Ebola outbreak was estimated in [16,17,19-21]. Althaus 2.5 [21]). [16] estimated R for EBOV using incidence data and The aforementioned modeling studies did not incorpo- a susceptible-exposed-infectious-recovered (SEIR) type rate the effect of traditional belief systems and customs model. The study emphasized the heightening of control on the transmission dynamics of EVD in the communi- measures in the three countries (especially in Liberia). ties (hence, they may have under estimated EVD burden). It should, however, be mentioned that the aforemen- The purpose of the current study is to assess the role tioned studies did not incorporate the role that disease of such belief systems and customs, and health-care set- transmission setting (community or health-care facil- tings, on the transmission dynamics of EVD in a pop- ities) plays in driving or curbing the spread of the ulation. To achieve this objective, a new deterministic disease. compartmental model, which incorporates the above and As evidenced by the current EBOV outbreaks in West other pertinent epidemiological, demographic and bio- Africa, the epidemiological setting, in which interaction logical aspects of EVD, is formulated. The specific goals and transmission between infected and susceptible indi- aretodetermine thekey factorsthatdrive thedisease viduals occur, plays an important role in the spread of transmission process and to propose effective and afford- the disease [2,10]. For example, health-care workers (doc- able strategies to curtail the spread of the disease. The tors, nurses and other paramedic workers who are at the paper is organized as follows. The model is formulated front lines of disease management and control) mostly in the section ‘Formulation of compartmental model’, acquire EVD infection in the hospital setting (or, in gen- and the worst-case scenario component of the model (in eral, health-care facilities), while caring for Ebola-infected the absence of intervention) is investigated in section patients [2,10,11]. They have a high risk of Ebola-induced ‘Pre-intervention model’. The full model is studied in mortality with 2,400 reported deaths among this group section ‘Assessment of basic control measures’, where the during this 2014 outbreak [22]. Furthermore, the models population-level impact of various effectiveness levels of Agusto et al. BMC Medicine (2015) 13:96 Page 4 of 17 a basic anti-Ebola public health control strategy are also non-hospitalized symptomatic (I (t)), hospitalized CN assessed. Discussion and recommendations stemming symptomatic (I (t)) and recovered individuals (R (t), CH C from the study (as well as general ones) are given in the R (t)). The population of individuals in health-care CH Conclusions. facilities consists of health-care workers in these facil- ities (as well as those who return to the community at the end of their shift at the hospital). In other Methods words, the population of individuals in the health- Formulation of compartmental model care facilities is sub-divided into susceptible/returning- This study is based on using a mathematical model, susceptible health-care workers (S (t), S (t)), exposed/ H RH parameterized using data for the 2014 EBOV outbreaks returning-exposed health-care workers (E (t), E (t)), H RH in Guinea, to gain insight into the transmission dynam- symptomatic/returning-symptomatic health-care work- ics of the disease within that nation. Since the 2014 Ebola ers (I (t), I (t)) and recovered/returning-recovered H RH outbreaks have been ongoing for nearly a year, the model health-care workers (R (t), R (t)). The model also H RH to be designed in this study incorporates demographic tracks the dynamics of the Ebola-infected deceased effects (and the relevant parameters,  and μ ,as C H individuals in the community and hospitals (D (t), described in Table 1, are estimated using census data from D (t)) and the cremated/buried Ebola-deceased individ- Guinea [31]). The model is formulated by splitting the uals (C (t)). The equations of the mathematical model are total population (of Guinea) into two main sub-groups, given (and described) in the appendix. A flow diagram of namely a sub-group of individuals in the community and the model is depicted in Figure 1, and the associated state another for those in health-care settings. variables and parameters are described in Tables 1 and 2. The population of individuals in the community con- Model (4), given in the appendix, extends the Ebola sists of individuals visiting loved ones (who are infected transmission models in [9,16] by (inter alia): with Ebola) in health-care facilities (notably hospitals) and the rest of the general public. This population is further The dynamics of health-care workers are included sub-divided into sub-populations of susceptible/visiting- (i.e., the role of the associated health-care setting). susceptible (S (t)/S (t)), exposed/visiting-exposed (E (t) C V C • The interaction between healthy (susceptible) /E (t)), symptomatic/visiting-symptomatic individuals individuals in a community and infected individuals in the early stage of EVD infection (I (t)/I (t)), CE VCE in a hospital, through visits, are accounted for. The effect of traditional (cultural) belief systems and customs that aid EVD transmission (such as the Table 1 Description of the state variables of the model handling of corpses during traditional burial in Figure 1 practices, etc.) are accounted for. This also entails the mistrust of members of the community for authority, Variable Description and fear and stereotypes against seeking medical care S (t)/S (t) Population of susceptible/visiting-susceptible C V (for fear of being quarantined, and/or acquiring individuals in the community infection during quarantine). E (t)/E (t) Population of exposed/visiting-exposed individuals in C V the community Furthermore, model (4) extends that in [18] by incorpo- I (t)/I (t) Population of symptomatic/visiting-symptomatic CE CEV individuals in the early stage of EBOV infection in the rating epidemiological compartments for, and dynamics community of, health-care workers and members of the general pub- I (t) Population of non-hospitalized symptomatic individuals CN lic who visit family members and/or acquaintances in I (t) Population of hospitalized symptomatic individuals hospitals, in addition to also including the role of tradi- CH tional belief systems and customs on EBOV transmission R (t), R (t), Population of recovered individuals in the community/ C CH R (t), R (t) health-care workers in the community and hospital H RH dynamics. Although model (4) is parameterized using data from Guinea [16], the parametrization is assumed to be S (t), S (t) Population of susceptible/returning-susceptible H RH health-care workers robust enough and applicable to the other two Ebola- E (t), E (t) Population of exposed/returning-exposed health-care stricken nations (Liberia and Sierra Leone). H RH workers I (t), I (t) Population of symptomatic/returning-symptomatic H RH Pre-intervention model health-care workers Model (4) is, first of all, studied for the special case D (t), D (t) Population of Ebola-deceased individuals in the C H where no public health interventions (i.e., no basic anti- community and hospital Ebola control measures and/or disease management in the C (t) Population of cremated/buried Ebola-deceased health-care settings) are implemented in the community. individuals In the absence of such interventions, model (4) reduces to Agusto et al. BMC Medicine (2015) 13:96 Page 5 of 17 Figure 1 Flow diagram of the model. the following basic (worst-case scenario) model (where a and 2. In particular, β is the effective contact (transmis- dot represents differentiation with respect to time): sion) rate, τ is a modification parameter that accounts for the assumed reduced infectiousness of Ebola-infected S (t) =  − λ (I , I , D )S (t) − μ S (t), C C C CE CN C C H C deceased individuals (in comparison to living individu- E (t) = λ (I , I , D ) S (t) − (σ + μ )E (t), C C CE CN C C C H C als with Ebola symptoms), and φ ≥ 1 is a modification I (t) = σ E (t) − (α + μ )I (t), parameter that accounts for the strength of the traditional CE C C C H CE belief systems and customs of the community members I (t) = α I (t) − (γ + μ )I (t),(1) CN C CE C H CN (that aid Ebola transmission). As stated above, the param- R (t) = hγ I (t) − μ R (t), C C CN H C eter φ models, for instance, the belief by some individuals D (t) = (1 − h)γ I (t) − δ D (t), C C CN C C within the Ebola-stricken nations that there is actually no C (t) = δ D (t), such thing as Ebola [23-25], that Ebola is merely govern- D C C ment propaganda [26] or, simply, the fear of being quar- where antined [27,28] or allowing their loved ones, who have β φ (I + I + τ D ) C C CE CN C C died of Ebola, to be cremated by public health officials λ (I , I , D ) = , C CE CN C S + E + I + I + R + D C C CE CN C C (burial squad) [27,29]. The overall effect of the traditional belief systems and customs parameter, φ , in model (1) (or is the infection rate of the disease (in the community), model (4)), is that it leads to the underreporting of new EBOV cases. It is worth re-emphasizing that earlier EBOV and all other parameters in λ are as defined in Tables 1 C Agusto et al. BMC Medicine (2015) 13:96 Page 6 of 17 Table 2 Description of the state parameters of the model Interpretation ofR in Figure 1 The basic reproduction number, given by Equation 2, can be rewritten in the following convenient form: Parameter Description β , β Effective contact (transmission) rate in the C H β φ σ β φ σ α β φ τ σ α γ (1 − h) community/hospital C C C C C C C C C C C C C R = + + . k k k k k k k k δ ,  ,  ,  Recruitment rates C RH V H 1 2 1 2 3 1 2 3 C (3) μ Natural death rate τ , τ , τ (i = 1, 2) Modification parameters for infectiousness C Ci Hi The epidemiological quantity, R , can be interpreted φ , φ Strengths of traditional belief systems and C H as follows. The first term in Equation 3 measures the customs in community and hospital average number of new cases generated by symptomatic σ , σ Progression rates of symptomatic individuals in the C H individuals in the early stage of EBOV infection (I ).It CE community and hospital is the product of the infection rate of susceptible indi- α , α Progression rates of early symptomatic individuals C H viduals in the community by members of the I group CE in the community and hospital ∗ ∗ ∗ ∗ (β φ S /N = β φ since N = S ), the probability that C C C C C P P C g Fraction of symptomatic individuals who are an exposed individual in the community survives the E hospitalized class and moves to the I class (σ /k )and theaverage CE C 1 h Fraction of symptomatic non-hospitalized duration in the I class (1/k ). individuals who recovered CE 2 The second term in Equation 3 accounts for the aver- f Fraction of symptomatic hospitalized individuals age number of new EBOV infections generated by non- who recovered hospitalized symptomatic individuals in the community ω , ω Hospitalization rates of symptomatic individuals CN RH in the community and health-care workers (I ). It is the product of the infection rate of susceptible CN individuals by the non-hospitalized symptomatic indi- ω Rate of escape from hospitalization CH ∗ ∗ viduals (β φ S /N = β φ ), the probability that an C C C C ε Efficacy of hospitalization in preventing the C exposed individual in the community survives the E class escape of Ebola-infected patients and transits to the I class (σ /k ), the probability that CE C 1 ε Efficacy of hospital-sanctioned burial (burial squad efficacy) an individual in the I classsurvivesthisclass andmoves CE to the I class (α /k ) and the average duration in the p Strength of cultural compliance/acceptance of CN C 2 the burial squad I class (1/k ). CN 3 Finally, the third term in Equation 3 represents the aver- γ , γ Recovery rates of symptomatic individuals in the C H community and hospital age number of new infections generated by Ebola-infected δ , δ Cremation/burial rates of Ebola-deceased deceased individuals in the community. It is the product C H individuals in the community and hospital of the infection rate of susceptible individuals by Ebola- ∗ ∗ ρ , ρ Transition rates of visitors between the community V RV deceased individuals (β φ τ S /N = β φ τ ), the C C C C C C C P and the hospital probability that an exposed individual in the community ρ , ρ Transition rates of health-care workers between H RH survives the E class (σ /k ) and moves to the I class, C C 1 CE the community and hospital the probability that an individual in the I class survives CE this class and transits to the I class (α /k ), the proba- CN C 2 models, such as those in [9,16,18], do not incorporate such bility that an individual in the I class did not survive at CN effects. the end of their time in this class, but died and moved to The associated basic reproduction number [32-35] of the D class (γ (1 − h)/k ), and the average duration in C C 3 model (1), denoted by R ,isgiven by 0 the cremated/buried class (1/δ ). The sum of these three terms gives the basic reproduc- β φ σ C C C R = [δ (α + k ) + τ α γ (1 − h)],(2) tion number,R . The disease can be effectively controlled 0 C C 3 C C C k k k δ 1 2 3 C if R is less than unity, and will persist if it exceeds unity. where k = σ + μ , k = α + μ , k = γ + μ and The numerical value (or range) of the threshold quan- 1 C H 2 C H 3 C H k = σ + μ . The epidemiological quantity, R ,mea- tityR is estimated using the parameter values and ranges 4 H H 0 0 sures the average number of Ebola cases generated by a tabulated in Table 3. While some of the parameter values typical Ebola-infected individual (living or dead but not in Table 3 were obtained from the literature, others were buried) introduced into a completely susceptible human estimated or fitted based on the EBOV data for Guinea, population [32-35]. Thus, EBOV can be effectively con- from 22 March to 29 August 2014 [16] (see Figure 2). For trolled in the community if the threshold quantity (R ) instance, the demographic parameter, μ ,isestimated as 0 H can be reduced to (and maintained at) a value less than μ = 1/58 per year, where 58 years is the average lifes- unity (i.e., R < 1). pan in Guinea [31]. The other demographic parameter, 0 Agusto et al. BMC Medicine (2015) 13:96 Page 7 of 17 Table 3 Values and ranges of the parameters in model (4)  , is then estimated as follows. Since the total popula- and model (1) tion of Guinea as at 2013 was 11,745,000 [31], we assumed that  /μ , which is the limiting total human popula- Parameter Baseline value Range Reference C H tion in the absence of the disease, is 11,745,000, so that β , β 0.3045 [0.2741 to 0.339]/day Fitted C H = 202500 per year. Consequently, using these param- 555/day Estimated eter estimates, we show, in this study, that the value of using [31] R for the 2014 Ebola outbreak in Guinea is R ≈ 1.46. 0 0 ,  ,  400/day [10 to 800]/day Variable RH V H Although this estimate is slightly lower than that reported μ 0.00004/day [1/[80 × 365] to [53,54] by Althaus [16] (who used the same data to estimateR ≈ 1/[58 × 365]]/day 1.51), it falls within the estimate of R ∈ [ 1, 2] given in ψ (1/10)/day [1/1,000 to 1]/day Assumed [16,19,20,36]. The fluctuations in the cumulative data in τ , τ , τ , 0.21/day [0.1 to 0.5]/day [55] C Ci Hi Figure 2 may be due to the correction of these numbers (by i = 1, 2 the World Health Organization (WHO)), as more reliable φ 1.2532 [1.1282 to 1.3785] Fitted data became available. φ 1 Fitted Sensitivity analysis σ , σ , σ 0.5239/day [0.4715 to 0.5763]/day Fitted C V H Sensitivity analysis [37-39] is carried out, on the param- α , α 0.5472/day [0.4925 to 0.6019]/day Fitted C H eters of model (1), to determine which of the parameters f , h 0.42, 0.48/day [0.42 to 0.8]/day [16,18] have the most significant impact on the outcome of the g 0.5/day [0.5 to 0.8]/day [18] numerical simulations of the model. Figure 3 depicts the ω , ω 0.21/day [0.1 to 0.5], Fitted CH CN partial rank correlation coefficient (PRCC) values for each [0.15 to 0.25]/day parameter of the model, using the ranges and baseline ω 0.5/day [0.5 to 1.0]/day Fitted RH values tabulated in Table 3 (with the basic reproduction ε 0.21/day [0.1 to 0.5]/day Variable number, R , as the response function). It follows from this figure that, in the absence of anti-Ebola public health γ , γ 0.5366/day [0.4829 to 0.5903]/day Fitted C H interventions, the parameters that have the most influ- δ , δ (1/2)/day [1/2 to 1]/day [18] C H ence on Ebola transmission dynamics in Guinea are the ρ , ρ 0.271/hour [0 to 1/2], 1/7/hour [55] V RV traditional/cultural/custom belief systems (φ ), the pro- ρ , ρ 0.071/hour [1/16 to 1/12], [55] H RH gression rate of early symptomatic individuals in the com- [1/12 to 1/8]/hour munity α , the effective contact rate (β ) and the recovery C C rate of symptomatic individuals in the community (γ ). Cases Deaths Mar 22 14 Apr 11 14 May 01 14 May 21 14 Jun 10 14 Jun 30 14 Jul 20 14 Aug 09 14 Aug 29 14 Dates Figure 2 Data fitting of the reported cumulative new cases and EBOV-induced mortality. The fitting used model (1). The data are for the 2014 EBOV outbreaks in Guinea (extracted from the World Health Organization website by Althaus [16]). The parameters fitted are given as β = 0.3045, σ = 0.5239, α = 0.5472, γ = 0.5366 and φ = 1.2532. (Approval was given by C. Althaus to use the data cited in [16]). C C C C Cumulative Number of Individuals for Guinea Agusto et al. BMC Medicine (2015) 13:96 Page 8 of 17 about a year after the start of the outbreak). In this case, the dominant parameters that positively impact the cumu- lative number of new cases are the recruitment rate into the community ( ) and the traditional/cultural/custom beliefs parameter (φ ) (these parameters remain dom- inant even after 18 months). Furthermore, the analy- sis was implemented using the cumulative number of new cases generated by Ebola-infected deceased individ- uals, showing, for this case, the dominant parameters to be the modification parameter associated with dis- ease transmission by Ebola-infected deceased individuals (τ ), the fraction of symptomatic individuals who recov- ered in the community (h) and the cremation parameter Figure 3 Partial rank correlation coefficient values for model (1). The (δ ); here, too, these parameters remain the dominant basic reproduction number (R ) was used as the response function. 0 ones 18 months after the initial outbreak. Surprisingly, the parameter associated with the detrimental role of the traditional/cultural/custom belief systems (φ )and the recruitment rate ( ) have only a marginal effect under this scenario. Hence, it follows from the above Thus, this study identifies the most important parame- ters that drive the transmission mechanism of the disease that the results obtained from the uncertainty/sensitivity in Guinea. The identification of these key parameters is analysis are dependent on the response/output function vital to the formulation of effective control strategies for chosen (it is, however, generally accepted thatR is a very combatting the spread of the disease. In other words, good determinant or predictor of disease burden during the results of this sensitivity analysis suggest that a strat- an epidemic or disease outbreak). egy that minimizes the impact of the traditional/cultural To quantify the expected burden of the disease in the beliefs and customs parameter (that is, reduce φ to a country (under the worst-case scenario), a box plot of the value closer to unity), reduces the progression rate of early distribution of R is generated, using the parameter val- symptomatic individuals (decrease α ), reduces the risk of ues and ranges in Table 3 with φ = 1.5. The results acquisition of Ebola infection in the community (reduce obtained, depicted in Figure 4a, show the distribution of β ) and increases the recovery rate (increase γ ) would the reproduction number in the range R ∈ [ 1.15, 2.05] C C be quite effective in curtailing the spread of the disease in (with a mean R ≈ 1.6, suggesting the potential for larger the country. Furthermore, these simulations suggest that EBOV outbreaks, in comparison to the case where such belief systems and customs had no detrimental effects, the 2014 EBOV outbreaks can be effectively controlled where one infected case infects, on average, about 1.6 oth- using basic (non-pharmaceutical) public health control ers). However, when the strength of the traditional beliefs measures (such as the aforementioned). and customs parameter is reduced to φ = 1.0 (i.e., people Sensitivity analysis was also carried out using the cumu- do not harbor detrimental traditional belief systems and lative number of new cases generated by symptomatic customs that aid Ebola transmission), the distribution of individuals in the community at time t = 360 days (i.e., (a) (b) 1.4 1.3 1.8 1.2 1.6 1.1 1.4 0.9 1.2 0.8 100 200 300 400 500 600 700 800 1000 100 200 300 400 500 600 700 800 1000 N (number of runs) N (number of runs) Figure 4 Box plot ofR for model (1). (a) Traditional belief systems and custom parameter, φ = 1.5. (b) Traditional belief systems and custom 0 C parameter, φ = 1. Parameter values (baseline) and ranges used are as given in Table 3. 0 Agusto et al. BMC Medicine (2015) 13:96 Page 9 of 17 R , depicted in Figure 4b, decreases to R ∈ [ 0.77, 1.35], proper handling of Ebola-infected deceased individu- 0 0 with a mean ofR ≈ 1 (corresponding to a much reduced als (before burial), etc. [29,40,41]. To increase recovery disease burden, in comparison to the former scenario with among infected people in the community (i.e., increase the φ = 1.5). It is evident from the box plots in Figure 4 fraction h), Ebola clinics and tents should be set up, and that the disease burden associated with the case where the populace encouraged to use them. Since EVD causes the belief systems and customs are taken into account high numbers of fatalities, in part due to dehydration of (Figure 4a) is at least 50% more than that for the case infected individuals [41] and lack of health-care facili- when these systems and customs do not induce any detri- ties, measures focused on providing adequate resources mental effect (Figure 4b). Furthermore, it is worth noting to such clinics or temporary make-shift tents for vis- that for φ = 1.5 (Figure 4a), the box plots are all right- its to patient will help increase the survival chances of skewed, with the central 50% of the generated R values Ebola-infected humans. While recruitment ( )intothe 0 C concentrated in the interval [ 1.36, 1.68], with the median community via immigration (movement) cannot be pre- close to the mean value, R = 1.5. Thus, large R val- vented (except in extreme cases [42]), the public health 0 0 ues, such as 2.1 and higher, will likely not be observed. agencies need to ensure that Ebola test units and clinics For the case when φ = 1.0 (Figure 4b), the box plots are in place at major points of entry, such as airports and are also right-skewed, with the central 50% of the gener- border crossings, and to discourage intra-city movement atedR values concentrated in the interval [ 0.9, 1.2], with of Ebola-infected individuals [40,43]. the median around R = 1. Nonetheless, these simula- tions emphasize the significant role the traditional beliefs Role of infectious living humans and Ebola-deceased and customs parameter (φ ) plays in the 2014 EBOV individuals outbreaks in Guinea. In this section, the contributions of EBOV-infected In summary, the aforementioned sensitivity analysis of (symptomatic) individuals in the early (I )and late (I ) CE CN model (1) suggests that control efforts should be focused stages of infectiousness on EBOV burden in the country on reducing the strength of the traditional beliefs and cus- will be quantified (for the case where no interventions are toms parameter (by reducing φ ), increasing recovery rate implemented). (by increasing γ ) and reducing transmission (via a reduc- Figure 5a shows that while the Ebola-infected deceased tion in β ). This can be achieved through a variety of individuals contribute about 22% of the total number of ways, such as a public health education/awareness cam- new infections, individuals in the early infection stage paign through media and radio advertisements, as well contribute about 33% and those in the late infection stage as door-to-door education of members of the commu- contribute the bulk of the infections (about 45%). This nity (to desensitize them against harboring such detri- figure underlines the significance of the role of poor mental traditional beliefs and customs). Furthermore, handling of Ebola-infected deceased individuals on the effective measures for curtailing disease transmission by transmission dynamics of the disease in the community. infected people in the community (i.e., minimizing β ) The effect of the traditional belief systems and customs and Ebola-infected deceased individuals (minimizing τ ) parameter (φ ) is further assessed by simulating model C C must be undertaken. This can be achieved by encouraging (1) using the parameters in Table 3 and various values the use of protective equipment by health-care workers, of φ . The results obtained, depicted in Figure 6, show, (a) (b) 4 5 x 10 x 10 Total number of new infections Total number of infections By I infectious 5 CE 12 By I infectious CE By I infectious CN By I infectious CN By D deceased 10 4 C By D deceased 0 0 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Time (days) Time (days) Figure 5 Simulations of model (1). (a) Total number of new cases generated by symptomatic living and deceased Ebola-infected individuals. (b) Cumulative number of new cases generated by symptomatic living and deceased Ebola-infected individuals. Parameter values used are as given in Table 3. Total number of new cases Cumulative number of new cases Agusto et al. BMC Medicine (2015) 13:96 Page 10 of 17 (a) (b) x 10 φ = 1.5 φ = 1.5 C C 4.5 φ = 1.3 φ = 1.3 C C φ = 1.2 φ = 1.2 C C 3.5 φ = 1.0 φ = 1.0 C C 2.5 1.5 0.5 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Time (days) Time (days) Figure 6 Simulations of model (1) with different values of φ = 1.5, 1.3, 1.2, 1.0. (a) Total number of new cases generated by symptomatic living individuals. (b) Total number of new cases generated by Ebola-infected deceased individuals. Parameter values used are as given in Table 3. as expected, that the total number of new cases gener- The total number of new cases generated by ated by symptomatic individuals (and associated peak) symptomatic living and Ebola-infected deceased increases with increasing values of φ (Figure 6a). Under individuals increases with increasing values of the this (worst-case) scenario, and with φ = 1.5 [21], the traditional beliefs and customs parameter (φ ). C C number of new Ebola cases peaks at about 49,560 after 72 The 2014 EVD is controllable using (affordable) basic days of the initial outbreak. Similar results were obtained public health control measures that focus on forthe totalnumberofnew casesgeneratedby theEbola- minimizing the strength of the detrimental infected deceased individuals (Figure 6b). These simu- traditional belief systems and customs in the affected lations further suggest, as expected, that a larger Ebola country, increasing the recovery rate and decreasing burden would have been recorded if effective anti-Ebola disease transmission. public health strategies were not implemented (in a timely manner). Assessment of basic control measures In summary, the simulations of the worst-case scenario The above analyses were implemented for the worst-case model (1) show that (in the absence of intervention): scenario. In practice, however, public health intervention strategies were implemented in an effort to combat effec- Traditional belief systems and customs play a vital tively the spread of EBOV in the affected countries (and, role in the 2014 Ebola outbreaks in Guinea (this by extension, globally). In this section, the population- would have resulted in about a 50% increase in the level impact of basic public health intervention strategies, disease burden recorded in Guinea, in the absence of on the disease dynamics in Guinea, is assessed. A sensi- basic public health control measures). tivity analysis is, first of all, carried out on the full model Ebola-infected deceased individuals contribute about (4), with the total number of surviving individuals (suscep- 22% of the total number of new infections, while tible and recovered) as the response (outcome) function. individuals in the early and later (symptomatic) Figure 7a shows the PRCC values for each parameter stages contribute about 33% and 45%, respectively. used in the sensitivity analysis. From this figure, it follows (a) (b) Figure 7 Partial rank correlation coefficient values of model (1). There were two response functions. (a) Total number of surviving individuals. (b) Total number of symptomatic individuals. Parameter values (baseline) and ranges used are as given in Table 3. Number of new cases generated by infectious Number of new cases generated deceased Agusto et al. BMC Medicine (2015) 13:96 Page 11 of 17 that for model (4), the dominant parameters are the hos- hospitals etc., which will be very effective in curtailing the pital escape rate of symptomatic individuals (ω ), the spread of EBOV. CH parameters for the strength of traditional/cultural/custom beliefs in the community and in health-care settings (φ Effectiveness levels of basic intervention strategy and φ ), the fraction of symptomatic individuals who Theprimaryaimofthisstudyis to assess theroleofbasic recovered in the community (h), the efficacy of hospi- (non-pharmaceutical) public health control measures for talization (ε) and the hospitalization rate of the non- effective containment of the 2014 EBOV outbreaks. As hospitalized symptomatic individuals (ω ). A similar noted by the WHO on the situation in Liberia, ‘the con- CN analysis was carried out using the total number of symp- ventional control interventions are not having adequate tomatic individuals as the response function, and the impact (in curtailing the spread of EVD) in the country, dominant parameters in this case (see Figure 7b) are the although they are effective in countries such as Nigeria, traditional/cultural/custom beliefs modification parame- Senegal, and the Democratic Republic of Congo with ters for the community and the health-care workers (φ limited transmission’ [44]. Following the results of the and φ ), the visitors’ mobility rates from the hospital back sensitivity analysis in section ‘Assessment of basic con- to the community (ρ ) and the progression rate of symp- trol measures’ above, the following effectiveness levels of RV tomatic individuals in the community and hospital (σ the basic public health control strategy against Ebola are and σ ). When the number of Ebola-infected deceased formulated. individuals is used as the response function, the dominant parameters are φ , φ , ρ , σ and σ (Figure 8a). Low-effectiveness level of the basic public health control H C RV C V Finally, when the number of Ebola-infected cre- strategy mated/buried individuals is chosen as the response func- The low-effectiveness level of the anti-Ebola control strat- tion, the key parameters (Figure 8b) are the escape rate egy assumes the strength of the community’s traditional/ from hospitalization of symptomatic individuals (ω ), cultural/custom belief systems to be 1.5 (i.e., φ = 1.5). CH the fraction of symptomatic individuals who recovered Recall that the beliefs parameter, φ ,captures, inter alia, in hospital (f ), the fraction of symptomatic individu- the community sentiments and reactions towards the dis- als who recovered in the community (h)and thetra- ease, the presence of shadow zones [28] and underreport- ditional/cultural/custom beliefs modification parameters ing [21,30]. It is assumed that hospitalized Ebola-infected of the community and the health-care workers (φ and individuals do not hold such traditional/cultural beliefs φ ). Again, these results further emphasize the sensitiv- (so that φ = 1). Furthermore, due to the relative high H H ity of the simulation (sensitivity analysis) results on the value of the beliefs parameter (φ ), it is plausible to response function chosen. These results show that a basic assume, under this low-effectiveness level of the control public health strategy that, in addition to the three aspects strategy, that some symptomatic individuals may choose identified under the worst-case scenario (i.e., decrease to escape from the isolation units after a day of hospital- φ to a value less than unity, increase recovery rate (γ ) ization (i.e., 1/ω = 1). Additionally, due to the social C C CH and decrease transmission rate (β )), also ensures that nature of and strong family ties in the affected communi- hospitalized people do not harbor detrimental traditional ties, it is assumed, for this effectiveness level, that com- beliefs (decrease φ to a value close to, or equal to, unity), munity members visiting their infected loved ones and/or will minimize the hospital escape rate (decrease ω acquaintances in health-care facilities stay at the facilities CH and ε), reduce the number and duration of visits in for an average period of 10 hours (i.e., 1/ρ = 1/ρ = V RV (a) (b) Figure 8 Partial rank correlation coefficient values of model (1). There were two response functions. (a) Total number of Ebola-infected deceased individuals. (b) Total number of Ebola-infected cremated/buried individuals. Parameter values (baseline) and ranges used are as given in Table 3. Agusto et al. BMC Medicine (2015) 13:96 Page 12 of 17 10 hours). Health-care workers and returning health-care The visiting period is reduced to 1 hour daily (i.e., 1/ρ = workers work daily 8-hour shifts (i.e., 1/ρ = 1/ρ = 1/ρ = 1 hour), and health-care workers and returning H RH RV 8 hours). For this effectiveness level, it is assumed that health-care workers work 24-hour shifts (i.e., ρ = ρ = H RH no transmission-reduction measures are implemented by 1 day). (It should be stated that requiring health-care the health-care workers or visitors in hospitals, and it is workers to work 24-hour shifts may not always be realis- further assumed that Ebola-infected deceased individuals tic, but the scarcity of such workers in some health-care transmit at the same rate as living symptomatic individu- settings may necessitate this.) Furthermore, the modifi- als (i.e., no extra care in handling Ebola-infected corpses). cation parameters for the infectiousness of symptomatic These assumptions lead to setting 1/ψ = 1/τ = individuals are reduced to 1/ψ = 100 and 1/τ = H C1 H C1 1/τ = 1/τ = 1. 1/τ = τ = 1000. The cremation/burial rates (δ C2 H1 C2 H1 C and δ ) are increased by 90% (so that δ = δ = H C H Moderate-effectiveness level of the basic public health 0.5 × 1.9). control strategy Figure 9a depicts the cumulative number of symp- For the moderate-effectiveness level of the anti-Ebola con- tomatic cases generated under the low-effectiveness level trol strategy, the community’s traditional/cultural/custom of the control strategy over a 200-day period, from beliefs parameter is reduced to 1.2 (i.e., φ = 1.2). Here, which it follows that nearly 380,000 cases would have the hospital (or health-care facility) escape rate of symp- been recorded. Figure 9b shows a dramatic reduc- tomatic individuals is increased to 3 days (i.e., 1/ω = 3 tion (to 92 and 50, respectively) under the moderate- CH days). Visiting periods were reduced to 3 hours daily (i.e., and high-effectiveness levels of the control strategy. It 1/ρ = 1/ρ = 3 hours), and health-care workers and is worth noting that although, as expected, the high- V RV returning health-care workers work daily 16-hour shifts effectiveness of the control strategy is far more effective (i.e., 1/ρ = 1/ρ = 16 hours). For this effectiveness in curtailing Ebola burden in the affected communi- H RH level, the modification parameters for the infectiousness ties, the moderate-effectiveness level of the strategy also of symptomatic individuals are reduced: 1/ψ = 10 and resulted in a dramatic decline in the number of cases 1/τ = 1/τ = 1/τ = 100. Lastly, the crema- in comparison to the low-effectiveness level. Similarly, C1 C2 H1 tion/burial rates of Ebola-infected deceased individuals the high-effectiveness level of this strategy is far more (δ and δ ) are increased by 50% (i.e., δ = δ = effective in reducing the cumulative Ebola-infected mor- C H C H 0.5 × 1.5). tality (Figures 10). These simulations clearly show that the 2014 Ebola outbreaks are controllable using basic pub- High-effectiveness level of the basic public health control lic health control measures, such as the moderate- and strategy high-effectiveness levels of the control strategy described For the high-effectiveness level of the anti-Ebola con- above. In particular, a 90% reduction in Ebola burden can be achieved by implementing basic control measures, trol strategy, the community’s traditional/cultural/custom such as: beliefs parameter is reduced to unity (i.e., these beliefs have no detrimental effect on Ebola transmission dynam- increasing the duration of health-care workers’ shifts ics). The escape rate of symptomatic individuals from isolation units is set to 20 days (i.e., 1/ω = 20 days). to 24 hours; CH (a) (b) x 10 low effectiveness level 3.5 moderate effectiveness level high effectiveness level 2.5 1.5 0.5 0 0 0 50 100 150 200 0 50 100 150 200 Time (days) Time (days) Figure 9 Simulations of model (4). The cumulative number of symptomatic cases generated under various effectiveness levels of the basic public health control strategy is shown. (a) Low-effectiveness level. (b) Moderate- and high-effectiveness levels. Other parameter values used are as given in Table 3. Cumulative number of symptomatic cases Agusto et al. BMC Medicine (2015) 13:96 Page 13 of 17 (a) (b) x 10 low effectiveness level moderate effectiveness level high effectiveness level 0 0 0 50 100 150 200 0 50 100 150 200 Time (days) Time (days) Figure 10 Simulations of model (4). The cumulative Ebola mortality for various effectiveness levels of the basic public health control strategy is shown. (a) Low-effectiveness level. (b) Moderate- and high-effectiveness levels. Parameter values used are as given in Table 3. reducing the duration of visits (of family members control measures (such as proper handling of Ebola- and acquaintances) to Ebola isolation units and wards infected patients and Ebola-deceased patients, limiting in hospitals/clinics/tents to 1 hour; the duration of family visits to health-care facilities to see reducing the strength of the community’s infected loved ones etc.). detrimental traditional/cultural/custom beliefs, fear, The study shows that, in the absence of public health mistrust and anger against public health authorities. interventions, the 2014 EBOV outbreaks would have had a much higher public health burden in Guinea (and, by It is worth stating that the above simulation results extension, the other affected countries). The distribution support the success story of Ebola control in Nigeria, of the basic reproduction number (R ), an epidemio- a country of over 170 million people and with a more logical threshold quantity that measures the spreading developed public health infrastructure (and largely edu- capacity of the disease, is estimated to lie in the range cated citizenry who are less amenable to harbor such [ 0.77, 1.35] when detrimental traditional belief systems detrimental traditional/cultural belief systems and cus- and customs are not at play, and within the range toms). Nigeria’s first case of Ebola was identified on 20 [ 1.15, 2.05] if such belief systems and customs are taken July 2014 (when a visitor flew into Lagos from Monrovia, into account. Traditional beliefs and customs played a Liberia, in search of anti-Ebola medical care) [2,4,45,46]. crucial role in fueling the 2014 EBOV outbreaks, since This resulted in 19 other cases and 8 deaths in total [47]. people in the Ebola-stricken communities generally did Nigeria was able to contain the spread of the virus [17,45- not adhere to the guidelines of the public health offi- 48] due, largely, to effective contract tracing of suspected cials. This was because of their mistrust of the authori- cases, monitoring of traced cases and isolating those with ties, thinking that Ebola was government propaganda or EBOV symptoms. Moreover, the people in the affected thinking that healthy people who go into quarantine may area (Lagos State, Nigeria) adhered, strictly, to the anti- become deliberately infected while in quarantine. Also, Ebola pronouncements and guidelines stipulated by the some isolated infected individuals choose to escape iso- public health officials (at such a dire time of immense fear) lation because of a fear of being cremated if they die, [45]. The WHO declared Nigeria to be Ebola-free on 20 rather than receiving a proper family burial. Further- October 2014 [49]. more, it is shown that the incorrect handling of Ebola- deceased individuals contributed to the spread of the disease (estimated to be about 22%; the rest of the infec- Results summary and discussion tions were generated by symptomatic individuals in the A new compartmental mathematical model, which strat- early stage of infection and those who chose not to go to ifies the total population into those in the community hospital). and those in health-care facilities, is designed and used to study the 2014 Ebola outbreaks in Guinea. The model This study identifies the main parameters that drove incorporates notable crucial features associated with dis- the 2014 EBOV outbreaks during the early (pre- ease transmission, such as the interaction between mem- intervention) phase of the disease, namely the tradi- bers of the community and their health-care settings, the tional/cultural/custom beliefs factor, the transmission rate role of Ebola-deceased individuals, and traditional belief (effective contact rate) of the disease and the recovery systems and customs. It is used to assess the population- rate of individuals in the community. The identifica- level impact of basic (non-pharmaceutical) public health tion of these crucial parameters helps in formulating Cumulative number of ebola−infected deceased Cumulative number of ebola−infected deceased Agusto et al. BMC Medicine (2015) 13:96 Page 14 of 17 an effective control strategy. For instance, a strategy concerted effort to control effectively the ongoing EBOV that minimizes the strength of the detrimental tradi- outbreaks in West Africa (particularly noting that a cure tional beliefs and customs parameter, as well as reduc- and an effective and safe vaccine against Ebola transmis- ing the transmission rate and increasing the recovery sion in humans remain elusive). rate would lead to effective community-wide control of the disease. The strength of the detrimental traditional/ Public health education and campaign: An effective cultural/custom belief systems can be reduced via an community-wide public health education campaign, effective community-wide public health education cam- which includes the local leaders (chiefs), has to be paign that involves the local chiefs and community lead- embarked upon in an effort to minimize the public ers. Transmission can be reduced by taking basic public mistrust, anger and apprehension against public health measures when caring for Ebola-infected individ- health authorities and officials who are fighting to uals, such as using well-trained health-care professionals end the transmission of EVD. Furthermore, and avoiding contact with infected bodily fluids. Trans- health-care workers must be trained in global best mission can also be reduced by proper handling of Ebola- practices, vis-à-vis the proper way to manage, handle deceased individuals. and care for Ebola-infected individuals and This study shows that the 2014 EBOV outbreaks are Ebola-deceased patients (to minimize infection controllable using basic (and affordable) public health among health-care professionals). This is in line with control measures. In particular, it is shown that a strat- the finding in this study that detrimental traditional egy that increases the length of shifts worked by health- belief systems and customs play a crucial role in the care workers caring for Ebola-infected patients to 24 2014 EBOV outbreaks. hours, limits the duration of visits of family members and Creation of Ebola response teams in local acquaintances to Ebola isolation units and wards to 1 hour communities: Each local community should have an and effectively minimizes the strength of the detrimental Ebola response team (the grassroots movement team) traditional beliefs and customs (that aid Ebola transmis- to help educate the populace about the disease and to sion) could lead to a dramatic reduction (over 90%) of the identify potential new cases and report them to public Ebola burden in the affected communities. We note that health agencies immediately. These local teams must while the feasibility of working a 24-hour shift is a tough be well trained. Confidence-building measures, to one to operationalize, it is not unheard of in the health- help them build the trust necessary within the care profession [50]. Moreover, in situations where there communities they serve, must be embarked upon. are extreme shortages of health-care professionals during With a generally weakened health-care system in a serious crisis, as in the three countries most affected by each of the three Ebola-stricken regions [2], the time the 2014 EVD epidemic, it would not be unusual to see it takes to isolate early symptomatic cases may be health-care workers working such uncommon shifts [51]. longer. To limit such a period, and hence minimize However, it is important to note that requiring a health- underreporting, such a response team can be the ears care worker to work a 24-hour shift is physically, mentally within the local communities. However, a prompt and emotionally stressful and may result in errors and response from the health-care officials responsible for mistakes in their health-care delivery to patients [51]. In transporting these potential new cases is necessary for urgent situations and crises were this might occur, plans the response team to achieve a meaningful impact. In should be made to ensure that health-care workers who addition, the response team should serve as a support work these shifts only do so for a few days consecutively, system to the local members. Such a team should also and that the nurses and health workers working these help convince family members of the need to release shifts organize their schedules and/or patient visits so that their Ebola-deceased relatives to the trained burial they, and their colleagues, get time to rest during the teams and help them mourn properly for their loved 24-hour period (and further adequate rest at the end of ones. They can also help minimize factors relating to their shift). In other words, this study shows that the 2014 traditional/cultural beliefs and customs through Ebola outbreaks is controllable using basic public health some of the aforementioned efforts. This will also interventions (provided they are of at least a moderate- play an important role in minimizing the detrimental effectiveness level, and are implemented effectively and effect of traditional belief systems and customs. consistently). Preparedness within households: Ebola is one of those rare diseases that forbids the natural love and Recommendations care, through touch, normally provided to sick loved We conclude by providing the following list of general ones in many cultures. It is difficult for some to see recommendations, mostly directly borne out of the sim- their vulnerable loved ones sick and yet be unable to ulation results derived from this study, can help in the help. That is generally a hard concept. To avoid such Agusto et al. BMC Medicine (2015) 13:96 Page 15 of 17 circumstances, each household should have a Ebola clinics for consultation were turned down prepared outline of actions to take if symptoms of because of a lack of beds [2]). Thus, more health-care EVD become evident within the household. First, tents and units are needed for the isolation and care health-care officials should be notified. If no one from of symptomatic patients, and support in the form of the health-care system comes to transport the engineers and construction volunteers would assist in symptomatic individual to a hospital, then while the setting up such temporary and permanent health family members are still able, they should be advised facilities and tents. This would provide space for more to go to a hospital immediately, avoiding crowds. In symptomatic individuals, reducing their numbers in the case of children who may not be identified early, community settings. Moreover, health-care one responsible adult, or a parent, should be given a professionals would be needed to staff these tents. protective suit to transport the child. In the case of late symptomatic individuals, only one designated member in the household should provide support to Appendix the sick human, even though the first step should be Appendix: Formulation of the general Ebola getting all patients to the hospital or some transmission model health-care facility. This will help early detection and We use a compartmental framework to model the trans- hospitalization of cases. mission dynamics of EVD in a population stratified into Social strategy: An unspoken feature that may impact two epidemiological settings: those in the community and transmission is the social structure associated with those within the health-care system. The population of the current Ebola outbreak. Families have lost income, susceptible members of the general public (S ) is gener- schools and businesses have been disrupted and most ated at the rate  (recruitment or birth). It is further foreign-owned companies have temporarily closed increased by the return of susceptible visitors from the down, and so the day-to-day functioning and needs hospital (at a rate ρ ). The population is decreased by RV of community members have been disrupted. To help infection (at a rate λ ), natural death (at a rate μ ;this cater for the day-to-day needs of communities rate is assumed for all epidemiological compartments) and quarantined, or the potential loss of income from visits to Ebola-infected relatives in health facilities, such reduced business and cultural activities, aid should be as hospitals, clinics, make-shift tent clinics, etc. (at a rate provided to these communities (this would help ρ ). The population of exposed (latent infected) members minimize the strength of the mistrust and fear against of the community (E ) is generated at the rate λ and C C public authorities, thereby minimizing EVD cases). decreased by development of clinical symptoms of Ebola Global strategy: In each of the three Ebola-stricken (at a rate σ ), natural death (at the rate μ )and visits to C H countries, health-care workers were overwhelmed infected relatives in health facilities (at the rate ρ ). It is [52]. Health-care facilities, which were weak in the increased by the return of the visitors (at a rate ρ ). RV first place, are now even more weakened [2]. Thus The population of early infectious individuals (I )is CE support, in the form of health-care professionals, generated at the rate σ and decreased by progression from the rest of the world would help to reinforce an to the non-hospitalized symptomatic class (at a rate overwhelmed health-care system and thus help in the (1 − g)α ,where g is the fraction of these individuals fight against EVD. Given the effects long work hours who are hospitalized), hospitalization (at a rate gα ), could have on the efficiency of health-care workers, natural death and visits (at the rate ρ ). It is increased such global support would help to increase the time by the return of the visitors (at the rate ρ ). The pop- RV period between daily work shifts of health-care ulation of non-hospitalized symptomatic individuals workers who are in direct contact with ebola infected (I ) is generated at the rate (1 − g)α .Itisfurther CN C patients, there by reducing their chances of becoming increased when hospitalized members of the commu- infected, which was shown, in this study, to be an nity escape from hospital (at a rate (1 − ε)ω ;where CN effective control tool against EVD. 0 <ε ≤ 1 is the efficacy of hospitalization to prevent Furthermore, support in the form of engineers and the escape of Ebola-infected patients). This population construction volunteers is also essential. With a is decreased by recovery (at a rate γ ), hospitalization weakened health-care system in the three Ebola- (at a rate ω ) and natural death. The population of CN stricken countries [2], the time it takes to isolate early recovered members of the community (R )isgenerated symptomatic cases and move them to a health-care at a rate hγ ,where h is the fraction of non-hospitalized setting may take longer due to a lack of trained symptomatic individuals who recovered (at the rate γ ; professionals to transport the symptomatic humans, and the remaining fraction, 1 − h,isdeceased).Itis or because of a lack of beds at health-care facilities reduced by natural death. The population of members (some of the early symptomatic cases that went to of the community who died of Ebola (D ) is generated C Agusto et al. BMC Medicine (2015) 13:96 Page 16 of 17 at the rate (1 − h)γ and is decreased by cremation (at a where, rate δ ). φ β (I + I + τ I + τ D ) The equations for the dynamics of health-care workers C C CE CN C1 RH C2 C λ (I , I , I , D ) = , C CE CN RH C (those in hospitals, or health-care facilities in general, and ψ φ β (I + I + I + τ D ) health-care workers who return to the community at the H H H CEV CH H H1 H λ (I , I , I , D ) = , H CEV CH H H end of their shift) are similarly derived (and not repeated P here). with N = S + E + I + I + R + D + S + E + P C C CE CN C C RH RH S (t) =  − λ (I , I , I , D )S (t) − μ S (t) C C C CE CN RH C C H C I + R + I + R +S + E + I + S + E + RH RH CH CH V V CEV H H I ++R + D + C . H H H D −ρ S + ρ S , V C RV V E (t) = λ (I , I , I , D )S (t) − (σ + μ )E (t) C C CE CN RH C C C H C Abbreviations EBOV, Ebola virus; EVD, Ebola virus disease; PRCC, partial rank correlation −ρ E (t) + ρ E (t), V C RV V coefficient; WHO, World Health Organization. I (t) = σ E (t) − (α + μ )I (t) − ρ I (t) CE C C C H CE V CE Competing interests +ρ I (t),(4) RV CEV The authors declare that they have no competing interests. I (t) = (1 − g)α I (t) + (1 − ε)ω I (t) CN C CE CH CH Authors’ contributions −(γ + ω + μ )I (t), C CN H CN All three authors (FBA, MIT-E and ABG) participated in the model building discussion. FBA and ABG carried out the mathematical analysis and numerical R (t) = hγ I (t) − μ R (t), C C CN H C simulations. All three authors (FBA, MIT-E and ABG) participated in the writing ˙ of the manuscript. All authors read, provided updates and approved the final D (t) = (1 − h)γ I (t) − δ D (t), C C CN C C version of the manuscript. Author details S (t) =  −λ (I , I , I , D )S (t)−μ S (t) RH RH H CE CN RH C RH H RH Department of Mathematics and Statistics, Austin Peay State University, Clarksville, TN 37044, USA. Department of Mathematics, Lehigh University, −ρ S (t) + ρ S (t), Bethlehem, PA 18015, USA. Simon A. Levin Mathematical, Computational and RH RH H H Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1904, E (t) = λ (I , I , I , D )S (t)−(σ +μ )E (t) 4 RH H CE CN RH C RH H H RH USA. School of Mathematical and Natural Sciences, Arizona State University, Phoenix, AZ 85069-7100, USA. −ρ E (t) + ρ E (t), RH RH H H Received: 2 December 2014 Accepted: 10 March 2015 I (t) = σ E (t) − (γ + μ )I (t) − ω I (t), RH H RH H H RH RH RH R (t) = γ I (t) − μ R − ρ R (t) + ρ R (t), RH H RH H RH RH RH H H References 1. Centers for Disease Control and Prevention. Outbreaks chronology: Ebola virus disease. http://www.cdc.gov/vhf/ebola/outbreaks/history/ I (t) = gα I (t) + ω I (t)−[ (1 − ε)ω + γ CH C CE CN CN CN H chronology.html. Accessed 1 Feb 2015. +μ ] I (t), H CH 2. World Health Organization. Ebola virus disease, fact sheet No 103. http:// www.who.int/mediacentre/factsheets/fs103/en/. Accessed 19 Oct 2014. R (t) = f γ I (t) − μ R (t), 3. Centers for Disease Control and Prevention. Outbreaks chronology: Ebola CH H CH H CH hemorrhagic fever. http://www.cdc.gov/vhf/Ebola/resources/outbreak- table.html. Accessed 25 Aug 2014. S (t) =  − λ (I , I , I , D )S (t) − μ S (t) V V H CEV CH H H V H V 4. Centers for Disease Control and Prevention. Ebola hemorrhagic fever. http://www.cdc.gov/vhf/Ebola/. Accessed 25 Aug 2014. −ρ S (t) + ρ S (t), RV V V C 5. Ebola crisis: outbreak death toll rises to 4 447saysWHO. BBC News Africa. http://www.bbc.com/news/world-africa-29615452. Accessed 15 Oct E (t) = λ (I , I , I , D )S (t) − (σ + μ )E (t) V H CEV CH H H V V H V 6. Centers for Disease Control and Prevention. 2014 Ebola outbreak in West −ρ E (t) + ρ E (t), RV V V C Africa. http://www.cdc.gov/vhf/Ebola/outbreaks/2014-west-africa/index. html. Accessed 19 Oct 2014. I (t) = σ E (t)−μ I (t)−ρ I (t)+ρ I (t), 7. World Health Organization. Ebola situation report. http://www.who.int/ V V H RV V CEV CEV CEV CE csr/disease/ebola/situation-reports/en/. Accessed 2 Feb 2015. ˙ 8. Bray M, Chertow DS. Epidemiology and pathogenesis of Ebola virus S (t) =  − λ (I , I , I , D )S (t) − μ S (t) H H H CEV CH H H H H H disease. UpToDate. 2015. http://www.uptodate.com/contents/ −ρ S (t) + ρ S (t), H H RH RH epidemiology-and-pathogenesis-of-ebola-virus-disease?topicKey=ID %2F3023&elapsedTimeMs=1&view=print&displayedView=full. E (t) = λ (I , I , I , D )S (t) − (σ + μ )E (t) H H CE CH H H H H H H 9. Chowell G, Hengartner NW, Castillo-Chavez C, Fenimore PW, Hyman JM. The basic reproductive number of Ebola and the effects of public health −ρ E (t) + ρ E (t), H H RH RH measures: the cases of Congo and Uganda. J Math Biol. 2004;28:503–22. I (t) = σ E (t) + ω I (t) − (γ + μ )I (t), H H H RH RH H H H 10. Centers for Disease Control and Prevention. Ebola hemorrhagic fever: fact sheet. http://www.cdc.gov/vhf/Ebola/pdf/Ebola-factsheet.pdf. Accessed R (t) = f γ I (t) − μ R (t) + ρ R (t)−ρ R (t), H H H H H RH RH H H 15 Oct 2014. ˙ 11. WHO Ebola Response Team. Ebola virus disease in West Africa – the first 9 D (t) = (1 − f )γ I (t) + (1 − f )γ I (t) − δ D (t), H H CH H H H H months of the epidemic and forward projections. N Engl J Med. 2014. C (t) = δ D (t) + δ D (t), D C C H H doi:10.1056/NEJMoa1411100. Agusto et al. BMC Medicine (2015) 13:96 Page 17 of 17 12. ZMapp manufactured by MAPP Biopharmaceuticals, Inc. 6160 Lusk Blvd. # 36. Gomes MFC, Pastore Y, Piontti A, Rossi L, Chao D, Longini I, et al. C105 San Diego, CA 92121. http://www.mappbio.com/. Assessing the international spreading risk associated with the 2014 West 13. TKM Ebola manufactured by Tekmira Pharmaceuticals Corporation. 100 - African Ebola outbreakPLOS Currents Outbreaks. 2014. 8900 Glenlyon Parkway Burnaby, British Columbia Canada V5J 5J8. http:// doi:10.1371/currents.outbreaks.cd818f63d40e24aef769dda7df9e0da5. www.tekmira.com/portfolio/tkm-ebola.php. 37. Blower SM, Dowlatabadi H. Sensitivity and uncertainty analysis of 14. Ebola in West Africa, 779. Lancet Infect Dis. 2014;14:. complex models of disease transmission: an HIV model, as an example. doi:10.1016/S1473-3099(14)70785-6. Int Stat Rev. 1994;2:229–43. 15. Quist-Arction O, Poon L. How a person can recover from Ebola. 2014. 38. Marino S, Hogue I B, Ray CJ, Kirschner DE. A methodology for performing http://www.npr.org/blogs/health/2014/04/11/301464924/how-a- global uncertainty and sensitivity analysis in systems biology. J Theor Biol. patient-can-recover-from-Ebola. Accessed 25 Aug 2014. 2008;254:178–96. http://dx.doi.org/10.1016/j.jtbi.2008.04.011. 16. Althaus CL. Estimating the reproduction number of Ebola virus (EVOB) 39. McLeod RG, Brewster JF, Gumel AB, Slonowsky DA. Sensitivity and during the 2014 outbreak in West Africa. PLOS Curr Outbreaks. 2014. uncertainty analyses for a SARS model with time-varying inputs and doi:10.1371/currents.outbreaks.91afb5e0f279e7f29e7056095255b288. outputs. Math Biosci Eng. 2006;3:527–44. 17. Fasina FO, Shittu A, Lazarus D, Tomori O, Simonsen L, Viboud C, et al. 40. Guinean who brought Ebola to Senegal recovered, to return. http://www. Transmission dynamics and control of Ebola virus disease outbreak in reuters.com/article/2014/09/10/us-health-ebola-senegal- Nigeria, July to September 2014. Eurosurveillance. 2014;19:9. idUSKBN0H50V720140910. Accessed May 1, 2015. 18. Legrand J, Grais RF, Boelle PY, Valleron AJ, Flahaut A. Understanding the 41. World Health Organization. Ebola virus disease. http://www.who.int/ dynamics of Ebola epidemics. Epidemiol Infect. 2007;135:610–21. mediacentre/factsheets/fs103/en/. Accessed 29 Sep 2014. 19. Nishiura H, Chowell G. Early transmission dynamics of Ebola virus disease 42. Roy-Macaulay C. Sierra Leone quarantines two million to fight Ebola. (EVD), West Africa. Eurosurveillance. 2014;19:pii=20894. Associated Press http://news.yahoo.com/sierra-leone-cordon-off-3- 20. Towers S, Patterson-Lomba O, Castillo-Chavez C. Temporal variations in areas-stop-ebola-085631264.html. Accessed 29 Sep 2014. the effective reproduction number of the 2014 West Africa Ebola 43. Mark M. Nigeria fears fourth Ebola frontline after infected man lands in Outbreak. PLOS Curr Outbreaks. 2014. Lagos. http://www.theguardian.com/world/2014/aug/13/ebola- doi:10.1371/currents.outbreaks.9e4c4294ec8ce1adad283172b16bc908. nigerian-capital. Accessed 29 Sep 2014. 21. Meltzer MI, Atkins CY, Santibanez S, Knust B, Petersen BW, Ervin ED, 44. World Health Organization. Ebola situation in Liberia: non-conventional et al. Estimating the future number of cases in the Ebola epidemic – interventions needed. http://www.who.int/mediacentre/news/ebola/8- Liberia and Sierra Leone, 2014–2015. Morb Mortal Wkly Rep. september-2014/en/. Accessed 9 Oct 2014. 2014;63:1–14. 45. How we managed Ebola outbreak – Fashola. Daily Independent. http:// 22. Health infectious disease: health group pleads for more workers to dailyindependentnig.com/2014/09/managed-Ebola-outbreak-fashola/. combat Ebola outbreak. Time. http://time.com/3340439/Ebola-outbreak- Accessed 9 Oct 2014. west-africa-who/. Accessed 19 Oct 2014. 46. Ebola: Fashola’s impressive leadership. Leadership. http://leadership.ng/ 23. Ebola patients flee as Liberia clinic looted. Al Jazeera. http://www. columns/386173/Ebola-fasholas-impressive-leadership. Accessed 9 Oct aljazeera.com/news/africa/2014/08/Ebola-patients-flee-as-liberia-clinic- looted-201481713725590885.html. Accessed 29 Sep 2014. 47. World Health Organization. Ebola response roadmap update: 17 October 24. Hogan C. There is no such thing as Ebola. Washington Post. http://www. 2014. http://apps.who.int/iris/bitstream/10665/136645/1/ washingtonpost.com/news/morning-mix/wp/2014/07/18/there-is-no- roadmapupdate17Oct14_eng.pdf?ua=1. Accessed 18 Oct 2014. such-thing-as-Ebola/. Accessed 14 Oct 2014. 48. World Health Organization. Ebola response roadmap update: 26 25. Wilson J. Eight killed in Guinea town over Ebola fears by CNN. 2014. September 2014. http://apps.who.int/iris/bitstream/10665/135029/1/ http://www.cnn.com/2014/09/19/health/Ebola-guinea-killing/index. roadmapupdate26sept14_eng.pdf?ua=1. Accessed 29 Sep 2014. html. Accessed 29 Sep 2014. 49. World Health Organization. WHO declares end of Ebola outbreak in 26. Jerving S. Why Liberians thought Ebola was a government scam to attract Nigeria. http://www.who.int/mediacentre/news/statements/2014/ western aid. Decades of corruption have left Liberians suspicious of their nigeria-ends-ebola/en/. Accessed 20 Oct 2014. government. The Nation. http://www.thenation.com/article/181618/ 50. National Association of Neonatal Nurse Practitioners. The impact of why-liberians-thought-Ebola-was-government-scam-attract-western- advanced practice nurses’ shift length and fatigue on patient safety. 2012. aid. Accessed 14 Oct 2014. http://www.nann.org/uploads/files/Fatigue_and_APRNs.pdf. Accessed 7 27. Bloch H. Denying Ebola turns out to be a very human response. http:// Mar 2015. www.npr.org/blogs/goatsandsoda/2014/09/27/350925364/denying- 51. US Department of Labor. Extended unusual work shifts. https://www. Ebola-turns-out-to-be-a-very-human-response. Accessed 14 Oct 2014. osha.gov/OshDoc/data_Hurricane_Facts/faq_longhours.html. Accessed 28. WHO warns of West Africa’s Ebola shadow zones. Al Jazeera. http://www. 6 Mar 2015. aljazeera.com/news/africa/2014/08/who-warns-africa-Ebola-shadow- 52. Centers for Disease Control and Prevention. Non-US healthcare settings: zones-2014822225018688250.html. Accessed 9 Oct 2014. international infection control and healthcare workers. http://www.cdc. 29. Meet the world’s bravest undertakers – Liberia’s Ebola burial squad. The gov/vhf/Ebola/hcp/non-us-healthcare-settings.html. Accessed 20 Oct Telegraph. http://www.telegraph.co.uk/news/worldnews/Ebola/ 2014. 11024042/Meet-the-worlds-bravest-undertakers-Liberias-Ebola-burial- 53. Chitnis N, Cushing JM, Hyman JM. Bifurcation analysis of a mathematical squad.html. Accessed 29 Sep 2014. model for malaria transmission. SIAM J Appl Math. 2006;67:24–45. 30. World Health Organization. WHO: Ebola Response Roadmap Situation 54. Niger AM, Gumel AB. Mathematical analysis of the role of repeated Report 1 October 2014. http://apps.who.int/iris/bitstream/10665/135600/ exposure on malaria transmission dynamics. Differential Equations 1/roadmapsitrep_1Oct2014_eng.pdf. Accessed May 1, 2015. Dynamical Syst. 2008;16:251–87. 31. World Health Organization. Guinea. http://www.who.int/countries/gin/ 55. Nuño M, Reichert TA, Chowell G, Gumel AB. Protecting residential care en/. Accessed 3 Feb 2015. facilities from pandemic influenza. PNAS. 2008;105:10625–30. 32. Anderson RM, May RM. Infectious diseases of humans. Oxford: Oxford University Press; 1991. 33. Diekmann O, Heesterbeek JAP, Metz JAP. On the definition and computation of the basic reproduction ratio R in models for infectious diseases in heterogeneous populations. J Theor Biol. 1990;229:119–26. 34. Hethcote HW. The mathematics of infectious diseases. SIAM Rev. 2000;42:599–653. 35. van den Driessche P, Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci. 2002l;180:29–48. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png BMC Medicine Springer Journals

Mathematical assessment of the effect of traditional beliefs and customs on the transmission dynamics of the 2014 Ebola outbreaks

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Springer Journals
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Copyright © 2015 by Agusto et al.; licensee BioMed Central.
Subject
Medicine & Public Health; Medicine/Public Health, general; Biomedicine, general
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1741-7015
DOI
10.1186/s12916-015-0318-3
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25902936
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Abstract

Background: Ebola is one of the most virulent human viral diseases, with a case fatality ratio between 25% to 90%. The 2014 West African outbreaks are the largest and worst in history. There is no specific treatment or effective/safe vaccine against the disease. Hence, control efforts are restricted to basic public health preventive (non-pharmaceutical) measures. Such efforts are undermined by traditional/cultural belief systems and customs, characterized by general mistrust and skepticism against government efforts to combat the disease. This study assesses the roles of traditional customs and public healthcare systems on the disease spread. Methods: A mathematical model is designed and used to assess population-level impact of basic non-pharmaceutical control measures on the 2014 Ebola outbreaks. The model incorporates the effects of traditional belief systems and customs, along with disease transmission within health-care settings and by Ebola-deceased individuals. A sensitivity analysis is performed to determine model parameters that most affect disease transmission. The model is parameterized using data from Guinea, one of the three Ebola-stricken countries. Numerical simulations are performed and the parameters that drive disease transmission, with or without basic public health control measures, determined. Three effectiveness levels of such basic measures are considered. Results: The distribution of the basic reproduction number (R ) for Guinea (in the absence of basic control measures) is such that R ∈ [ 0.77, 1.35], for the case when the belief systems do not result in more unreported Ebola cases. When such systems inhibit control efforts, the distribution increases to R ∈ [ 1.15, 2.05]. The total Ebola cases are contributed by Ebola-deceased individuals (22%), symptomatic individuals in the early (33%) and latter (45%) infection stages. A significant reduction of new Ebola cases can be achieved by increasing health-care workers’ daily shifts from 8 to 24 hours, limiting hospital visitation to 1 hour and educating the populace to abandon detrimental traditional/cultural belief systems. Conclusions: The 2014 outbreaks are controllable using a moderately-effective basic public health intervention strategy alone. A much higher (> 50%) disease burden would have been recorded in the absence of such intervention. 2000 Mathematics Subject Classifications: 92B05, 93A30, 93C15. Keywords: Ebola, Community, Hospital, Health-care workers, Quarantine *Correspondence: agumel@asu.edu Simon A. Levin Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1904, USA School of Mathematical and Natural Sciences, Arizona State University, Phoenix, AZ 85069-7100, USA Full list of author information is available at the end of the article © 2015 Agusto et al.; licensee BioMed Central. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Agusto et al. BMC Medicine (2015) 13:96 Page 2 of 17 Background vessels, rendering the blood vessels to be more perme- Ebola virus disease (EVD), caused by Ebola virus (EBOV) able. The increased permeability causes the blood vessels and formerly known as Ebola hemorrhagic fever, is one to leak out blood [8]. The virus also evades the host’s nat- of the world’s most virulent diseases. The disease, which ural defense system, by infecting immune cells, a channel spreads in human and other mammalian populations, has through which it is transported to other body parts and a case fatality ratio from 25% to 90% in humans [1,2]. organs, such as the liver, spleen, kidney and brain [8]. The The first known case of EVD dates back to 1976, where virus can cause these organs to fail, leading to death of the two outbreaks occurred (in Sudan and in the Democratic infected human host. Republic of Congo, formerly Zaire; the later outbreak was Ebola-infected humans typically exhibit flu-like symp- identified near the Ebola River, where the disease got its toms during the initial phase of the infection [8], and can name [2,3]). Since then, other outbreaks have occurred, have, or progress to, other symptoms such as fever, severe most notably in parts of Central Africa [3]. However, the headache, muscle aches, weakness, vomiting, diarrhea, largest, and most devastating, outbreak of EVD is the 2014 stomach pains, loss of appetite and, at times, bleeding epidemic in three West African countries (Guinea, Liberia (which may be visible or internal) [8,10,11]. An infected and Sierra Leone). This EVD outbreak (believed to have human is infectious (i.e., capable of transmitting the dis- started in Guinea in March 2014 [2]) is the first to have ease to susceptible individuals) at the onset of symptoms occurred in West Africa [4]. [2,8]. Transmission typically occurs when a susceptible The disease, which also spread to Nigeria (started by an human comes into contact with virus-infected fluids, such airline passenger, who arrived from Liberia) and Senegal as blood, bodily secretions (e.g., feces, saliva, vomit, urine, (started by a student from Guinea, who arrived by land semen and sweat), organs or bodily fluids of an infected transportation) [2,4], spread to other regions outside human (dead or alive) [2,10]. Contact with such fluids Africa. For instance, some Ebola-infected patients were may be as a result of direct contact between suscepti- flown to the US, France, Germany, Norway, Spain and the ble and infected humans, or due to indirect contact with UK [5] for health-care delivery. The US diagnosed its first environments contaminated with the aforementioned flu- imported travel-related Ebola case in September 2014 (by ids [2]. Individuals with high risk of exposure to EBOV a person who had travelled to Dallas, Texas, from Liberia). are the immediate family members of Ebola-infected The imported case, who later died of the disease on 8 humans and health-care workers who treat Ebola-infected October 2014, resulted in the infection of two health-care patients. workers who cared for the deceased patient [6]. One of In the absence of a cure (a specific treatment) or effec- the cases flown to Spain also led to an infection of health- tive and safe vaccine against the spread of EBOV in care workers [5]. Additionally, a separate Ebola outbreak, humans, anti-Ebola control efforts are mostly restricted unrelated to the West African outbreaks, occurred in the to basic public health preventive measures, disease Democratic Republic of Congo [2]. By 15 October 2014, management and treatment of Ebola-related symptoms. the case count for the 2014 EVD was 8,997 with 4,493 Public health preventive measures include approved fatalities [6] (a case fatality ratio of about 50%). It should health-care techniques practiced by health-care workers be mentioned that these estimates include the cases for when dealing with Ebola-infected patients, or, in areas Nigeria, Senegal, Spain and the USA [7]. These num- around Ebola-infected patients, educating the public and bers increased to 15,935 and 5,689, respectively (36% case raising awareness of the disease, quarantine of suspected fatality ratio) by 23 November 2014. The latest update, cases, isolation of symptomatic cases, rapid laboratory dated 21 January 2015, shows a case count of 21,724 diagnostic tests, minimizing contact with bodily fluids, and 8,641 fatalities (representing a case fatality ratio of wearing protective equipment by health-care providers 40%) [7]. and proper handling of individuals who died of the Ebola The natural reservoir and host of the EBOV is consid- virus [2,10]. The disease management component of the ered (albeit not yet proven [4]) to be fruit bats of the control strategy (for infected patients) typically entails the Pteropodidae family [2]. It is hypothesized that the virus administration of intravenous fluids and balancing elec- is introduced into the human population when a human trolytes to hydrate the patient, the maintenance of oxygen comes into contact with the blood, organ secretions or levels and blood pressure, and possibly a transfusion with bodily fluids of an animal infected with the EBOV. The blood from a matching Ebola survivor [4]. incubation period of EBOV is between 2 and 21 days Recovery from the disease is possible (but the rate of [2,8,9] (although some studies have estimated the most recovery tends to be lower than that of the Ebola-induced common incubation period to be 8 to 10 days [10]). Dur- death rate [11]). Note that some experimental drugs (such ing the incubation period, the virus infects body cells, as ZMapp [12] and TKM Ebola [13]) and vaccines are replicates and bursts out of the infected cells, produc- being developed for use in humans (in fact, ZMapp was ing EBOV glycoproteins that attach to the inside of blood reportedly used to treat the two American volunteers Agusto et al. BMC Medicine (2015) 13:96 Page 3 of 17 who contracted the disease while in missionary service in in [9,16,17,19,20] did not account for disease spread by Liberia, although its safety and efficacy have not yet been Ebola-infected deceased individuals (prior to, or during, tested on humans [14]). However, a person’s best chances their burial or cremation), a feature that is known to play of survival, following the acquisition of the infection, is a major role in the current outbreaks [2]. Legrand et al. early diagnosis (and prompt and effective disease man- [18] developed a compartmental model, using data from agement). This is challenging, however, since the early the 1995 Democratic Republic of Congo and 2000 Uganda symptoms of Ebola are similar to those of some other dis- Ebola epidemic outbreaks. The model allowed for EBOV eases, such as malaria and typhoid fever (diseases that are transmission by infected humans in both the community endemic in the region ravaged by the 2014 EBOV out- and the hospital. breaks [10]). However, using approved laboratory tests, a Another important feature that plays a critical role in the definitive diagnosis of EBOV can be made [2]. It is known 2014 EVD outbreaks is traditional/cultural belief systems that Ebola infection confers permanent natural immu- and customs. For instance, while some individuals in the nity (in individuals who have recovered from the disease) three Ebola-stricken nations believe that there is no Ebola against re-infection [15]. Although a human may be clini- [23-25], others claim that it is government propaganda to cally cleared of the virus (i.e., is declared to be recovered), attract more foreign aid dollars [26], control the popu- a male may, however, still have the virus in his semen for 2 lation or harvest human organs [27]. Furthermore, some to 3 months [2,15], and it may be found in the breast milk susceptible members of the public (including those at high of breast-feeding mothers [15]. risk of EBOV infection) refuse to be quarantined because A number of mathematical models and statistical meth- of their belief, or fear, that they might be deliberately odshavebeenusedinanattempt to understand the infected during quarantine [27,28]. There is also a fear that transmission dynamics of EVD (see for instance [9,16-20], they will notbeabletogivealovedone whodiedofEbola and some of the references therein). In [9], a compart- a proper traditional burial (since Ebola-infected humans mental mathematical model was used to estimate the who die in hospitals are typically cremated [26,27,29], number of secondary cases generated by an index case a practice that is not accepted by those who harbor a (the basic reproduction number), in the absence or pres- belief in traditional burial rituals). Adherence to these ence of control measures, for the 1995 Congo and 2000 traditional/cultural beliefs and customs often leads some Uganda Ebola outbreaks. The study further highlighted family members to hide Ebola-infected loved ones (to the importance of basic public health control measures, evade the health-care system), resulting in the develop- such as public health education, contact tracing and quar- ment of shadow zones [28], where paramedics cannot antine of suspected cases, and the role such measures visit, and, invariably, resulting in significant underreport- can play in reducing the final size of the epidemics. Most ing of EVD cases [21,30] (the Centers for Disease Control recently, the basic reproduction number for the 2014 estimated a potential underreporting correction factor of Ebola outbreak was estimated in [16,17,19-21]. Althaus 2.5 [21]). [16] estimated R for EBOV using incidence data and The aforementioned modeling studies did not incorpo- a susceptible-exposed-infectious-recovered (SEIR) type rate the effect of traditional belief systems and customs model. The study emphasized the heightening of control on the transmission dynamics of EVD in the communi- measures in the three countries (especially in Liberia). ties (hence, they may have under estimated EVD burden). It should, however, be mentioned that the aforemen- The purpose of the current study is to assess the role tioned studies did not incorporate the role that disease of such belief systems and customs, and health-care set- transmission setting (community or health-care facil- tings, on the transmission dynamics of EVD in a pop- ities) plays in driving or curbing the spread of the ulation. To achieve this objective, a new deterministic disease. compartmental model, which incorporates the above and As evidenced by the current EBOV outbreaks in West other pertinent epidemiological, demographic and bio- Africa, the epidemiological setting, in which interaction logical aspects of EVD, is formulated. The specific goals and transmission between infected and susceptible indi- aretodetermine thekey factorsthatdrive thedisease viduals occur, plays an important role in the spread of transmission process and to propose effective and afford- the disease [2,10]. For example, health-care workers (doc- able strategies to curtail the spread of the disease. The tors, nurses and other paramedic workers who are at the paper is organized as follows. The model is formulated front lines of disease management and control) mostly in the section ‘Formulation of compartmental model’, acquire EVD infection in the hospital setting (or, in gen- and the worst-case scenario component of the model (in eral, health-care facilities), while caring for Ebola-infected the absence of intervention) is investigated in section patients [2,10,11]. They have a high risk of Ebola-induced ‘Pre-intervention model’. The full model is studied in mortality with 2,400 reported deaths among this group section ‘Assessment of basic control measures’, where the during this 2014 outbreak [22]. Furthermore, the models population-level impact of various effectiveness levels of Agusto et al. BMC Medicine (2015) 13:96 Page 4 of 17 a basic anti-Ebola public health control strategy are also non-hospitalized symptomatic (I (t)), hospitalized CN assessed. Discussion and recommendations stemming symptomatic (I (t)) and recovered individuals (R (t), CH C from the study (as well as general ones) are given in the R (t)). The population of individuals in health-care CH Conclusions. facilities consists of health-care workers in these facil- ities (as well as those who return to the community at the end of their shift at the hospital). In other Methods words, the population of individuals in the health- Formulation of compartmental model care facilities is sub-divided into susceptible/returning- This study is based on using a mathematical model, susceptible health-care workers (S (t), S (t)), exposed/ H RH parameterized using data for the 2014 EBOV outbreaks returning-exposed health-care workers (E (t), E (t)), H RH in Guinea, to gain insight into the transmission dynam- symptomatic/returning-symptomatic health-care work- ics of the disease within that nation. Since the 2014 Ebola ers (I (t), I (t)) and recovered/returning-recovered H RH outbreaks have been ongoing for nearly a year, the model health-care workers (R (t), R (t)). The model also H RH to be designed in this study incorporates demographic tracks the dynamics of the Ebola-infected deceased effects (and the relevant parameters,  and μ ,as C H individuals in the community and hospitals (D (t), described in Table 1, are estimated using census data from D (t)) and the cremated/buried Ebola-deceased individ- Guinea [31]). The model is formulated by splitting the uals (C (t)). The equations of the mathematical model are total population (of Guinea) into two main sub-groups, given (and described) in the appendix. A flow diagram of namely a sub-group of individuals in the community and the model is depicted in Figure 1, and the associated state another for those in health-care settings. variables and parameters are described in Tables 1 and 2. The population of individuals in the community con- Model (4), given in the appendix, extends the Ebola sists of individuals visiting loved ones (who are infected transmission models in [9,16] by (inter alia): with Ebola) in health-care facilities (notably hospitals) and the rest of the general public. This population is further The dynamics of health-care workers are included sub-divided into sub-populations of susceptible/visiting- (i.e., the role of the associated health-care setting). susceptible (S (t)/S (t)), exposed/visiting-exposed (E (t) C V C • The interaction between healthy (susceptible) /E (t)), symptomatic/visiting-symptomatic individuals individuals in a community and infected individuals in the early stage of EVD infection (I (t)/I (t)), CE VCE in a hospital, through visits, are accounted for. The effect of traditional (cultural) belief systems and customs that aid EVD transmission (such as the Table 1 Description of the state variables of the model handling of corpses during traditional burial in Figure 1 practices, etc.) are accounted for. This also entails the mistrust of members of the community for authority, Variable Description and fear and stereotypes against seeking medical care S (t)/S (t) Population of susceptible/visiting-susceptible C V (for fear of being quarantined, and/or acquiring individuals in the community infection during quarantine). E (t)/E (t) Population of exposed/visiting-exposed individuals in C V the community Furthermore, model (4) extends that in [18] by incorpo- I (t)/I (t) Population of symptomatic/visiting-symptomatic CE CEV individuals in the early stage of EBOV infection in the rating epidemiological compartments for, and dynamics community of, health-care workers and members of the general pub- I (t) Population of non-hospitalized symptomatic individuals CN lic who visit family members and/or acquaintances in I (t) Population of hospitalized symptomatic individuals hospitals, in addition to also including the role of tradi- CH tional belief systems and customs on EBOV transmission R (t), R (t), Population of recovered individuals in the community/ C CH R (t), R (t) health-care workers in the community and hospital H RH dynamics. Although model (4) is parameterized using data from Guinea [16], the parametrization is assumed to be S (t), S (t) Population of susceptible/returning-susceptible H RH health-care workers robust enough and applicable to the other two Ebola- E (t), E (t) Population of exposed/returning-exposed health-care stricken nations (Liberia and Sierra Leone). H RH workers I (t), I (t) Population of symptomatic/returning-symptomatic H RH Pre-intervention model health-care workers Model (4) is, first of all, studied for the special case D (t), D (t) Population of Ebola-deceased individuals in the C H where no public health interventions (i.e., no basic anti- community and hospital Ebola control measures and/or disease management in the C (t) Population of cremated/buried Ebola-deceased health-care settings) are implemented in the community. individuals In the absence of such interventions, model (4) reduces to Agusto et al. BMC Medicine (2015) 13:96 Page 5 of 17 Figure 1 Flow diagram of the model. the following basic (worst-case scenario) model (where a and 2. In particular, β is the effective contact (transmis- dot represents differentiation with respect to time): sion) rate, τ is a modification parameter that accounts for the assumed reduced infectiousness of Ebola-infected S (t) =  − λ (I , I , D )S (t) − μ S (t), C C C CE CN C C H C deceased individuals (in comparison to living individu- E (t) = λ (I , I , D ) S (t) − (σ + μ )E (t), C C CE CN C C C H C als with Ebola symptoms), and φ ≥ 1 is a modification I (t) = σ E (t) − (α + μ )I (t), parameter that accounts for the strength of the traditional CE C C C H CE belief systems and customs of the community members I (t) = α I (t) − (γ + μ )I (t),(1) CN C CE C H CN (that aid Ebola transmission). As stated above, the param- R (t) = hγ I (t) − μ R (t), C C CN H C eter φ models, for instance, the belief by some individuals D (t) = (1 − h)γ I (t) − δ D (t), C C CN C C within the Ebola-stricken nations that there is actually no C (t) = δ D (t), such thing as Ebola [23-25], that Ebola is merely govern- D C C ment propaganda [26] or, simply, the fear of being quar- where antined [27,28] or allowing their loved ones, who have β φ (I + I + τ D ) C C CE CN C C died of Ebola, to be cremated by public health officials λ (I , I , D ) = , C CE CN C S + E + I + I + R + D C C CE CN C C (burial squad) [27,29]. The overall effect of the traditional belief systems and customs parameter, φ , in model (1) (or is the infection rate of the disease (in the community), model (4)), is that it leads to the underreporting of new EBOV cases. It is worth re-emphasizing that earlier EBOV and all other parameters in λ are as defined in Tables 1 C Agusto et al. BMC Medicine (2015) 13:96 Page 6 of 17 Table 2 Description of the state parameters of the model Interpretation ofR in Figure 1 The basic reproduction number, given by Equation 2, can be rewritten in the following convenient form: Parameter Description β , β Effective contact (transmission) rate in the C H β φ σ β φ σ α β φ τ σ α γ (1 − h) community/hospital C C C C C C C C C C C C C R = + + . k k k k k k k k δ ,  ,  ,  Recruitment rates C RH V H 1 2 1 2 3 1 2 3 C (3) μ Natural death rate τ , τ , τ (i = 1, 2) Modification parameters for infectiousness C Ci Hi The epidemiological quantity, R , can be interpreted φ , φ Strengths of traditional belief systems and C H as follows. The first term in Equation 3 measures the customs in community and hospital average number of new cases generated by symptomatic σ , σ Progression rates of symptomatic individuals in the C H individuals in the early stage of EBOV infection (I ).It CE community and hospital is the product of the infection rate of susceptible indi- α , α Progression rates of early symptomatic individuals C H viduals in the community by members of the I group CE in the community and hospital ∗ ∗ ∗ ∗ (β φ S /N = β φ since N = S ), the probability that C C C C C P P C g Fraction of symptomatic individuals who are an exposed individual in the community survives the E hospitalized class and moves to the I class (σ /k )and theaverage CE C 1 h Fraction of symptomatic non-hospitalized duration in the I class (1/k ). individuals who recovered CE 2 The second term in Equation 3 accounts for the aver- f Fraction of symptomatic hospitalized individuals age number of new EBOV infections generated by non- who recovered hospitalized symptomatic individuals in the community ω , ω Hospitalization rates of symptomatic individuals CN RH in the community and health-care workers (I ). It is the product of the infection rate of susceptible CN individuals by the non-hospitalized symptomatic indi- ω Rate of escape from hospitalization CH ∗ ∗ viduals (β φ S /N = β φ ), the probability that an C C C C ε Efficacy of hospitalization in preventing the C exposed individual in the community survives the E class escape of Ebola-infected patients and transits to the I class (σ /k ), the probability that CE C 1 ε Efficacy of hospital-sanctioned burial (burial squad efficacy) an individual in the I classsurvivesthisclass andmoves CE to the I class (α /k ) and the average duration in the p Strength of cultural compliance/acceptance of CN C 2 the burial squad I class (1/k ). CN 3 Finally, the third term in Equation 3 represents the aver- γ , γ Recovery rates of symptomatic individuals in the C H community and hospital age number of new infections generated by Ebola-infected δ , δ Cremation/burial rates of Ebola-deceased deceased individuals in the community. It is the product C H individuals in the community and hospital of the infection rate of susceptible individuals by Ebola- ∗ ∗ ρ , ρ Transition rates of visitors between the community V RV deceased individuals (β φ τ S /N = β φ τ ), the C C C C C C C P and the hospital probability that an exposed individual in the community ρ , ρ Transition rates of health-care workers between H RH survives the E class (σ /k ) and moves to the I class, C C 1 CE the community and hospital the probability that an individual in the I class survives CE this class and transits to the I class (α /k ), the proba- CN C 2 models, such as those in [9,16,18], do not incorporate such bility that an individual in the I class did not survive at CN effects. the end of their time in this class, but died and moved to The associated basic reproduction number [32-35] of the D class (γ (1 − h)/k ), and the average duration in C C 3 model (1), denoted by R ,isgiven by 0 the cremated/buried class (1/δ ). The sum of these three terms gives the basic reproduc- β φ σ C C C R = [δ (α + k ) + τ α γ (1 − h)],(2) tion number,R . The disease can be effectively controlled 0 C C 3 C C C k k k δ 1 2 3 C if R is less than unity, and will persist if it exceeds unity. where k = σ + μ , k = α + μ , k = γ + μ and The numerical value (or range) of the threshold quan- 1 C H 2 C H 3 C H k = σ + μ . The epidemiological quantity, R ,mea- tityR is estimated using the parameter values and ranges 4 H H 0 0 sures the average number of Ebola cases generated by a tabulated in Table 3. While some of the parameter values typical Ebola-infected individual (living or dead but not in Table 3 were obtained from the literature, others were buried) introduced into a completely susceptible human estimated or fitted based on the EBOV data for Guinea, population [32-35]. Thus, EBOV can be effectively con- from 22 March to 29 August 2014 [16] (see Figure 2). For trolled in the community if the threshold quantity (R ) instance, the demographic parameter, μ ,isestimated as 0 H can be reduced to (and maintained at) a value less than μ = 1/58 per year, where 58 years is the average lifes- unity (i.e., R < 1). pan in Guinea [31]. The other demographic parameter, 0 Agusto et al. BMC Medicine (2015) 13:96 Page 7 of 17 Table 3 Values and ranges of the parameters in model (4)  , is then estimated as follows. Since the total popula- and model (1) tion of Guinea as at 2013 was 11,745,000 [31], we assumed that  /μ , which is the limiting total human popula- Parameter Baseline value Range Reference C H tion in the absence of the disease, is 11,745,000, so that β , β 0.3045 [0.2741 to 0.339]/day Fitted C H = 202500 per year. Consequently, using these param- 555/day Estimated eter estimates, we show, in this study, that the value of using [31] R for the 2014 Ebola outbreak in Guinea is R ≈ 1.46. 0 0 ,  ,  400/day [10 to 800]/day Variable RH V H Although this estimate is slightly lower than that reported μ 0.00004/day [1/[80 × 365] to [53,54] by Althaus [16] (who used the same data to estimateR ≈ 1/[58 × 365]]/day 1.51), it falls within the estimate of R ∈ [ 1, 2] given in ψ (1/10)/day [1/1,000 to 1]/day Assumed [16,19,20,36]. The fluctuations in the cumulative data in τ , τ , τ , 0.21/day [0.1 to 0.5]/day [55] C Ci Hi Figure 2 may be due to the correction of these numbers (by i = 1, 2 the World Health Organization (WHO)), as more reliable φ 1.2532 [1.1282 to 1.3785] Fitted data became available. φ 1 Fitted Sensitivity analysis σ , σ , σ 0.5239/day [0.4715 to 0.5763]/day Fitted C V H Sensitivity analysis [37-39] is carried out, on the param- α , α 0.5472/day [0.4925 to 0.6019]/day Fitted C H eters of model (1), to determine which of the parameters f , h 0.42, 0.48/day [0.42 to 0.8]/day [16,18] have the most significant impact on the outcome of the g 0.5/day [0.5 to 0.8]/day [18] numerical simulations of the model. Figure 3 depicts the ω , ω 0.21/day [0.1 to 0.5], Fitted CH CN partial rank correlation coefficient (PRCC) values for each [0.15 to 0.25]/day parameter of the model, using the ranges and baseline ω 0.5/day [0.5 to 1.0]/day Fitted RH values tabulated in Table 3 (with the basic reproduction ε 0.21/day [0.1 to 0.5]/day Variable number, R , as the response function). It follows from this figure that, in the absence of anti-Ebola public health γ , γ 0.5366/day [0.4829 to 0.5903]/day Fitted C H interventions, the parameters that have the most influ- δ , δ (1/2)/day [1/2 to 1]/day [18] C H ence on Ebola transmission dynamics in Guinea are the ρ , ρ 0.271/hour [0 to 1/2], 1/7/hour [55] V RV traditional/cultural/custom belief systems (φ ), the pro- ρ , ρ 0.071/hour [1/16 to 1/12], [55] H RH gression rate of early symptomatic individuals in the com- [1/12 to 1/8]/hour munity α , the effective contact rate (β ) and the recovery C C rate of symptomatic individuals in the community (γ ). Cases Deaths Mar 22 14 Apr 11 14 May 01 14 May 21 14 Jun 10 14 Jun 30 14 Jul 20 14 Aug 09 14 Aug 29 14 Dates Figure 2 Data fitting of the reported cumulative new cases and EBOV-induced mortality. The fitting used model (1). The data are for the 2014 EBOV outbreaks in Guinea (extracted from the World Health Organization website by Althaus [16]). The parameters fitted are given as β = 0.3045, σ = 0.5239, α = 0.5472, γ = 0.5366 and φ = 1.2532. (Approval was given by C. Althaus to use the data cited in [16]). C C C C Cumulative Number of Individuals for Guinea Agusto et al. BMC Medicine (2015) 13:96 Page 8 of 17 about a year after the start of the outbreak). In this case, the dominant parameters that positively impact the cumu- lative number of new cases are the recruitment rate into the community ( ) and the traditional/cultural/custom beliefs parameter (φ ) (these parameters remain dom- inant even after 18 months). Furthermore, the analy- sis was implemented using the cumulative number of new cases generated by Ebola-infected deceased individ- uals, showing, for this case, the dominant parameters to be the modification parameter associated with dis- ease transmission by Ebola-infected deceased individuals (τ ), the fraction of symptomatic individuals who recov- ered in the community (h) and the cremation parameter Figure 3 Partial rank correlation coefficient values for model (1). The (δ ); here, too, these parameters remain the dominant basic reproduction number (R ) was used as the response function. 0 ones 18 months after the initial outbreak. Surprisingly, the parameter associated with the detrimental role of the traditional/cultural/custom belief systems (φ )and the recruitment rate ( ) have only a marginal effect under this scenario. Hence, it follows from the above Thus, this study identifies the most important parame- ters that drive the transmission mechanism of the disease that the results obtained from the uncertainty/sensitivity in Guinea. The identification of these key parameters is analysis are dependent on the response/output function vital to the formulation of effective control strategies for chosen (it is, however, generally accepted thatR is a very combatting the spread of the disease. In other words, good determinant or predictor of disease burden during the results of this sensitivity analysis suggest that a strat- an epidemic or disease outbreak). egy that minimizes the impact of the traditional/cultural To quantify the expected burden of the disease in the beliefs and customs parameter (that is, reduce φ to a country (under the worst-case scenario), a box plot of the value closer to unity), reduces the progression rate of early distribution of R is generated, using the parameter val- symptomatic individuals (decrease α ), reduces the risk of ues and ranges in Table 3 with φ = 1.5. The results acquisition of Ebola infection in the community (reduce obtained, depicted in Figure 4a, show the distribution of β ) and increases the recovery rate (increase γ ) would the reproduction number in the range R ∈ [ 1.15, 2.05] C C be quite effective in curtailing the spread of the disease in (with a mean R ≈ 1.6, suggesting the potential for larger the country. Furthermore, these simulations suggest that EBOV outbreaks, in comparison to the case where such belief systems and customs had no detrimental effects, the 2014 EBOV outbreaks can be effectively controlled where one infected case infects, on average, about 1.6 oth- using basic (non-pharmaceutical) public health control ers). However, when the strength of the traditional beliefs measures (such as the aforementioned). and customs parameter is reduced to φ = 1.0 (i.e., people Sensitivity analysis was also carried out using the cumu- do not harbor detrimental traditional belief systems and lative number of new cases generated by symptomatic customs that aid Ebola transmission), the distribution of individuals in the community at time t = 360 days (i.e., (a) (b) 1.4 1.3 1.8 1.2 1.6 1.1 1.4 0.9 1.2 0.8 100 200 300 400 500 600 700 800 1000 100 200 300 400 500 600 700 800 1000 N (number of runs) N (number of runs) Figure 4 Box plot ofR for model (1). (a) Traditional belief systems and custom parameter, φ = 1.5. (b) Traditional belief systems and custom 0 C parameter, φ = 1. Parameter values (baseline) and ranges used are as given in Table 3. 0 Agusto et al. BMC Medicine (2015) 13:96 Page 9 of 17 R , depicted in Figure 4b, decreases to R ∈ [ 0.77, 1.35], proper handling of Ebola-infected deceased individu- 0 0 with a mean ofR ≈ 1 (corresponding to a much reduced als (before burial), etc. [29,40,41]. To increase recovery disease burden, in comparison to the former scenario with among infected people in the community (i.e., increase the φ = 1.5). It is evident from the box plots in Figure 4 fraction h), Ebola clinics and tents should be set up, and that the disease burden associated with the case where the populace encouraged to use them. Since EVD causes the belief systems and customs are taken into account high numbers of fatalities, in part due to dehydration of (Figure 4a) is at least 50% more than that for the case infected individuals [41] and lack of health-care facili- when these systems and customs do not induce any detri- ties, measures focused on providing adequate resources mental effect (Figure 4b). Furthermore, it is worth noting to such clinics or temporary make-shift tents for vis- that for φ = 1.5 (Figure 4a), the box plots are all right- its to patient will help increase the survival chances of skewed, with the central 50% of the generated R values Ebola-infected humans. While recruitment ( )intothe 0 C concentrated in the interval [ 1.36, 1.68], with the median community via immigration (movement) cannot be pre- close to the mean value, R = 1.5. Thus, large R val- vented (except in extreme cases [42]), the public health 0 0 ues, such as 2.1 and higher, will likely not be observed. agencies need to ensure that Ebola test units and clinics For the case when φ = 1.0 (Figure 4b), the box plots are in place at major points of entry, such as airports and are also right-skewed, with the central 50% of the gener- border crossings, and to discourage intra-city movement atedR values concentrated in the interval [ 0.9, 1.2], with of Ebola-infected individuals [40,43]. the median around R = 1. Nonetheless, these simula- tions emphasize the significant role the traditional beliefs Role of infectious living humans and Ebola-deceased and customs parameter (φ ) plays in the 2014 EBOV individuals outbreaks in Guinea. In this section, the contributions of EBOV-infected In summary, the aforementioned sensitivity analysis of (symptomatic) individuals in the early (I )and late (I ) CE CN model (1) suggests that control efforts should be focused stages of infectiousness on EBOV burden in the country on reducing the strength of the traditional beliefs and cus- will be quantified (for the case where no interventions are toms parameter (by reducing φ ), increasing recovery rate implemented). (by increasing γ ) and reducing transmission (via a reduc- Figure 5a shows that while the Ebola-infected deceased tion in β ). This can be achieved through a variety of individuals contribute about 22% of the total number of ways, such as a public health education/awareness cam- new infections, individuals in the early infection stage paign through media and radio advertisements, as well contribute about 33% and those in the late infection stage as door-to-door education of members of the commu- contribute the bulk of the infections (about 45%). This nity (to desensitize them against harboring such detri- figure underlines the significance of the role of poor mental traditional beliefs and customs). Furthermore, handling of Ebola-infected deceased individuals on the effective measures for curtailing disease transmission by transmission dynamics of the disease in the community. infected people in the community (i.e., minimizing β ) The effect of the traditional belief systems and customs and Ebola-infected deceased individuals (minimizing τ ) parameter (φ ) is further assessed by simulating model C C must be undertaken. This can be achieved by encouraging (1) using the parameters in Table 3 and various values the use of protective equipment by health-care workers, of φ . The results obtained, depicted in Figure 6, show, (a) (b) 4 5 x 10 x 10 Total number of new infections Total number of infections By I infectious 5 CE 12 By I infectious CE By I infectious CN By I infectious CN By D deceased 10 4 C By D deceased 0 0 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Time (days) Time (days) Figure 5 Simulations of model (1). (a) Total number of new cases generated by symptomatic living and deceased Ebola-infected individuals. (b) Cumulative number of new cases generated by symptomatic living and deceased Ebola-infected individuals. Parameter values used are as given in Table 3. Total number of new cases Cumulative number of new cases Agusto et al. BMC Medicine (2015) 13:96 Page 10 of 17 (a) (b) x 10 φ = 1.5 φ = 1.5 C C 4.5 φ = 1.3 φ = 1.3 C C φ = 1.2 φ = 1.2 C C 3.5 φ = 1.0 φ = 1.0 C C 2.5 1.5 0.5 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Time (days) Time (days) Figure 6 Simulations of model (1) with different values of φ = 1.5, 1.3, 1.2, 1.0. (a) Total number of new cases generated by symptomatic living individuals. (b) Total number of new cases generated by Ebola-infected deceased individuals. Parameter values used are as given in Table 3. as expected, that the total number of new cases gener- The total number of new cases generated by ated by symptomatic individuals (and associated peak) symptomatic living and Ebola-infected deceased increases with increasing values of φ (Figure 6a). Under individuals increases with increasing values of the this (worst-case) scenario, and with φ = 1.5 [21], the traditional beliefs and customs parameter (φ ). C C number of new Ebola cases peaks at about 49,560 after 72 The 2014 EVD is controllable using (affordable) basic days of the initial outbreak. Similar results were obtained public health control measures that focus on forthe totalnumberofnew casesgeneratedby theEbola- minimizing the strength of the detrimental infected deceased individuals (Figure 6b). These simu- traditional belief systems and customs in the affected lations further suggest, as expected, that a larger Ebola country, increasing the recovery rate and decreasing burden would have been recorded if effective anti-Ebola disease transmission. public health strategies were not implemented (in a timely manner). Assessment of basic control measures In summary, the simulations of the worst-case scenario The above analyses were implemented for the worst-case model (1) show that (in the absence of intervention): scenario. In practice, however, public health intervention strategies were implemented in an effort to combat effec- Traditional belief systems and customs play a vital tively the spread of EBOV in the affected countries (and, role in the 2014 Ebola outbreaks in Guinea (this by extension, globally). In this section, the population- would have resulted in about a 50% increase in the level impact of basic public health intervention strategies, disease burden recorded in Guinea, in the absence of on the disease dynamics in Guinea, is assessed. A sensi- basic public health control measures). tivity analysis is, first of all, carried out on the full model Ebola-infected deceased individuals contribute about (4), with the total number of surviving individuals (suscep- 22% of the total number of new infections, while tible and recovered) as the response (outcome) function. individuals in the early and later (symptomatic) Figure 7a shows the PRCC values for each parameter stages contribute about 33% and 45%, respectively. used in the sensitivity analysis. From this figure, it follows (a) (b) Figure 7 Partial rank correlation coefficient values of model (1). There were two response functions. (a) Total number of surviving individuals. (b) Total number of symptomatic individuals. Parameter values (baseline) and ranges used are as given in Table 3. Number of new cases generated by infectious Number of new cases generated deceased Agusto et al. BMC Medicine (2015) 13:96 Page 11 of 17 that for model (4), the dominant parameters are the hos- hospitals etc., which will be very effective in curtailing the pital escape rate of symptomatic individuals (ω ), the spread of EBOV. CH parameters for the strength of traditional/cultural/custom beliefs in the community and in health-care settings (φ Effectiveness levels of basic intervention strategy and φ ), the fraction of symptomatic individuals who Theprimaryaimofthisstudyis to assess theroleofbasic recovered in the community (h), the efficacy of hospi- (non-pharmaceutical) public health control measures for talization (ε) and the hospitalization rate of the non- effective containment of the 2014 EBOV outbreaks. As hospitalized symptomatic individuals (ω ). A similar noted by the WHO on the situation in Liberia, ‘the con- CN analysis was carried out using the total number of symp- ventional control interventions are not having adequate tomatic individuals as the response function, and the impact (in curtailing the spread of EVD) in the country, dominant parameters in this case (see Figure 7b) are the although they are effective in countries such as Nigeria, traditional/cultural/custom beliefs modification parame- Senegal, and the Democratic Republic of Congo with ters for the community and the health-care workers (φ limited transmission’ [44]. Following the results of the and φ ), the visitors’ mobility rates from the hospital back sensitivity analysis in section ‘Assessment of basic con- to the community (ρ ) and the progression rate of symp- trol measures’ above, the following effectiveness levels of RV tomatic individuals in the community and hospital (σ the basic public health control strategy against Ebola are and σ ). When the number of Ebola-infected deceased formulated. individuals is used as the response function, the dominant parameters are φ , φ , ρ , σ and σ (Figure 8a). Low-effectiveness level of the basic public health control H C RV C V Finally, when the number of Ebola-infected cre- strategy mated/buried individuals is chosen as the response func- The low-effectiveness level of the anti-Ebola control strat- tion, the key parameters (Figure 8b) are the escape rate egy assumes the strength of the community’s traditional/ from hospitalization of symptomatic individuals (ω ), cultural/custom belief systems to be 1.5 (i.e., φ = 1.5). CH the fraction of symptomatic individuals who recovered Recall that the beliefs parameter, φ ,captures, inter alia, in hospital (f ), the fraction of symptomatic individu- the community sentiments and reactions towards the dis- als who recovered in the community (h)and thetra- ease, the presence of shadow zones [28] and underreport- ditional/cultural/custom beliefs modification parameters ing [21,30]. It is assumed that hospitalized Ebola-infected of the community and the health-care workers (φ and individuals do not hold such traditional/cultural beliefs φ ). Again, these results further emphasize the sensitiv- (so that φ = 1). Furthermore, due to the relative high H H ity of the simulation (sensitivity analysis) results on the value of the beliefs parameter (φ ), it is plausible to response function chosen. These results show that a basic assume, under this low-effectiveness level of the control public health strategy that, in addition to the three aspects strategy, that some symptomatic individuals may choose identified under the worst-case scenario (i.e., decrease to escape from the isolation units after a day of hospital- φ to a value less than unity, increase recovery rate (γ ) ization (i.e., 1/ω = 1). Additionally, due to the social C C CH and decrease transmission rate (β )), also ensures that nature of and strong family ties in the affected communi- hospitalized people do not harbor detrimental traditional ties, it is assumed, for this effectiveness level, that com- beliefs (decrease φ to a value close to, or equal to, unity), munity members visiting their infected loved ones and/or will minimize the hospital escape rate (decrease ω acquaintances in health-care facilities stay at the facilities CH and ε), reduce the number and duration of visits in for an average period of 10 hours (i.e., 1/ρ = 1/ρ = V RV (a) (b) Figure 8 Partial rank correlation coefficient values of model (1). There were two response functions. (a) Total number of Ebola-infected deceased individuals. (b) Total number of Ebola-infected cremated/buried individuals. Parameter values (baseline) and ranges used are as given in Table 3. Agusto et al. BMC Medicine (2015) 13:96 Page 12 of 17 10 hours). Health-care workers and returning health-care The visiting period is reduced to 1 hour daily (i.e., 1/ρ = workers work daily 8-hour shifts (i.e., 1/ρ = 1/ρ = 1/ρ = 1 hour), and health-care workers and returning H RH RV 8 hours). For this effectiveness level, it is assumed that health-care workers work 24-hour shifts (i.e., ρ = ρ = H RH no transmission-reduction measures are implemented by 1 day). (It should be stated that requiring health-care the health-care workers or visitors in hospitals, and it is workers to work 24-hour shifts may not always be realis- further assumed that Ebola-infected deceased individuals tic, but the scarcity of such workers in some health-care transmit at the same rate as living symptomatic individu- settings may necessitate this.) Furthermore, the modifi- als (i.e., no extra care in handling Ebola-infected corpses). cation parameters for the infectiousness of symptomatic These assumptions lead to setting 1/ψ = 1/τ = individuals are reduced to 1/ψ = 100 and 1/τ = H C1 H C1 1/τ = 1/τ = 1. 1/τ = τ = 1000. The cremation/burial rates (δ C2 H1 C2 H1 C and δ ) are increased by 90% (so that δ = δ = H C H Moderate-effectiveness level of the basic public health 0.5 × 1.9). control strategy Figure 9a depicts the cumulative number of symp- For the moderate-effectiveness level of the anti-Ebola con- tomatic cases generated under the low-effectiveness level trol strategy, the community’s traditional/cultural/custom of the control strategy over a 200-day period, from beliefs parameter is reduced to 1.2 (i.e., φ = 1.2). Here, which it follows that nearly 380,000 cases would have the hospital (or health-care facility) escape rate of symp- been recorded. Figure 9b shows a dramatic reduc- tomatic individuals is increased to 3 days (i.e., 1/ω = 3 tion (to 92 and 50, respectively) under the moderate- CH days). Visiting periods were reduced to 3 hours daily (i.e., and high-effectiveness levels of the control strategy. It 1/ρ = 1/ρ = 3 hours), and health-care workers and is worth noting that although, as expected, the high- V RV returning health-care workers work daily 16-hour shifts effectiveness of the control strategy is far more effective (i.e., 1/ρ = 1/ρ = 16 hours). For this effectiveness in curtailing Ebola burden in the affected communi- H RH level, the modification parameters for the infectiousness ties, the moderate-effectiveness level of the strategy also of symptomatic individuals are reduced: 1/ψ = 10 and resulted in a dramatic decline in the number of cases 1/τ = 1/τ = 1/τ = 100. Lastly, the crema- in comparison to the low-effectiveness level. Similarly, C1 C2 H1 tion/burial rates of Ebola-infected deceased individuals the high-effectiveness level of this strategy is far more (δ and δ ) are increased by 50% (i.e., δ = δ = effective in reducing the cumulative Ebola-infected mor- C H C H 0.5 × 1.5). tality (Figures 10). These simulations clearly show that the 2014 Ebola outbreaks are controllable using basic pub- High-effectiveness level of the basic public health control lic health control measures, such as the moderate- and strategy high-effectiveness levels of the control strategy described For the high-effectiveness level of the anti-Ebola con- above. In particular, a 90% reduction in Ebola burden can be achieved by implementing basic control measures, trol strategy, the community’s traditional/cultural/custom such as: beliefs parameter is reduced to unity (i.e., these beliefs have no detrimental effect on Ebola transmission dynam- increasing the duration of health-care workers’ shifts ics). The escape rate of symptomatic individuals from isolation units is set to 20 days (i.e., 1/ω = 20 days). to 24 hours; CH (a) (b) x 10 low effectiveness level 3.5 moderate effectiveness level high effectiveness level 2.5 1.5 0.5 0 0 0 50 100 150 200 0 50 100 150 200 Time (days) Time (days) Figure 9 Simulations of model (4). The cumulative number of symptomatic cases generated under various effectiveness levels of the basic public health control strategy is shown. (a) Low-effectiveness level. (b) Moderate- and high-effectiveness levels. Other parameter values used are as given in Table 3. Cumulative number of symptomatic cases Agusto et al. BMC Medicine (2015) 13:96 Page 13 of 17 (a) (b) x 10 low effectiveness level moderate effectiveness level high effectiveness level 0 0 0 50 100 150 200 0 50 100 150 200 Time (days) Time (days) Figure 10 Simulations of model (4). The cumulative Ebola mortality for various effectiveness levels of the basic public health control strategy is shown. (a) Low-effectiveness level. (b) Moderate- and high-effectiveness levels. Parameter values used are as given in Table 3. reducing the duration of visits (of family members control measures (such as proper handling of Ebola- and acquaintances) to Ebola isolation units and wards infected patients and Ebola-deceased patients, limiting in hospitals/clinics/tents to 1 hour; the duration of family visits to health-care facilities to see reducing the strength of the community’s infected loved ones etc.). detrimental traditional/cultural/custom beliefs, fear, The study shows that, in the absence of public health mistrust and anger against public health authorities. interventions, the 2014 EBOV outbreaks would have had a much higher public health burden in Guinea (and, by It is worth stating that the above simulation results extension, the other affected countries). The distribution support the success story of Ebola control in Nigeria, of the basic reproduction number (R ), an epidemio- a country of over 170 million people and with a more logical threshold quantity that measures the spreading developed public health infrastructure (and largely edu- capacity of the disease, is estimated to lie in the range cated citizenry who are less amenable to harbor such [ 0.77, 1.35] when detrimental traditional belief systems detrimental traditional/cultural belief systems and cus- and customs are not at play, and within the range toms). Nigeria’s first case of Ebola was identified on 20 [ 1.15, 2.05] if such belief systems and customs are taken July 2014 (when a visitor flew into Lagos from Monrovia, into account. Traditional beliefs and customs played a Liberia, in search of anti-Ebola medical care) [2,4,45,46]. crucial role in fueling the 2014 EBOV outbreaks, since This resulted in 19 other cases and 8 deaths in total [47]. people in the Ebola-stricken communities generally did Nigeria was able to contain the spread of the virus [17,45- not adhere to the guidelines of the public health offi- 48] due, largely, to effective contract tracing of suspected cials. This was because of their mistrust of the authori- cases, monitoring of traced cases and isolating those with ties, thinking that Ebola was government propaganda or EBOV symptoms. Moreover, the people in the affected thinking that healthy people who go into quarantine may area (Lagos State, Nigeria) adhered, strictly, to the anti- become deliberately infected while in quarantine. Also, Ebola pronouncements and guidelines stipulated by the some isolated infected individuals choose to escape iso- public health officials (at such a dire time of immense fear) lation because of a fear of being cremated if they die, [45]. The WHO declared Nigeria to be Ebola-free on 20 rather than receiving a proper family burial. Further- October 2014 [49]. more, it is shown that the incorrect handling of Ebola- deceased individuals contributed to the spread of the disease (estimated to be about 22%; the rest of the infec- Results summary and discussion tions were generated by symptomatic individuals in the A new compartmental mathematical model, which strat- early stage of infection and those who chose not to go to ifies the total population into those in the community hospital). and those in health-care facilities, is designed and used to study the 2014 Ebola outbreaks in Guinea. The model This study identifies the main parameters that drove incorporates notable crucial features associated with dis- the 2014 EBOV outbreaks during the early (pre- ease transmission, such as the interaction between mem- intervention) phase of the disease, namely the tradi- bers of the community and their health-care settings, the tional/cultural/custom beliefs factor, the transmission rate role of Ebola-deceased individuals, and traditional belief (effective contact rate) of the disease and the recovery systems and customs. It is used to assess the population- rate of individuals in the community. The identifica- level impact of basic (non-pharmaceutical) public health tion of these crucial parameters helps in formulating Cumulative number of ebola−infected deceased Cumulative number of ebola−infected deceased Agusto et al. BMC Medicine (2015) 13:96 Page 14 of 17 an effective control strategy. For instance, a strategy concerted effort to control effectively the ongoing EBOV that minimizes the strength of the detrimental tradi- outbreaks in West Africa (particularly noting that a cure tional beliefs and customs parameter, as well as reduc- and an effective and safe vaccine against Ebola transmis- ing the transmission rate and increasing the recovery sion in humans remain elusive). rate would lead to effective community-wide control of the disease. The strength of the detrimental traditional/ Public health education and campaign: An effective cultural/custom belief systems can be reduced via an community-wide public health education campaign, effective community-wide public health education cam- which includes the local leaders (chiefs), has to be paign that involves the local chiefs and community lead- embarked upon in an effort to minimize the public ers. Transmission can be reduced by taking basic public mistrust, anger and apprehension against public health measures when caring for Ebola-infected individ- health authorities and officials who are fighting to uals, such as using well-trained health-care professionals end the transmission of EVD. Furthermore, and avoiding contact with infected bodily fluids. Trans- health-care workers must be trained in global best mission can also be reduced by proper handling of Ebola- practices, vis-à-vis the proper way to manage, handle deceased individuals. and care for Ebola-infected individuals and This study shows that the 2014 EBOV outbreaks are Ebola-deceased patients (to minimize infection controllable using basic (and affordable) public health among health-care professionals). This is in line with control measures. In particular, it is shown that a strat- the finding in this study that detrimental traditional egy that increases the length of shifts worked by health- belief systems and customs play a crucial role in the care workers caring for Ebola-infected patients to 24 2014 EBOV outbreaks. hours, limits the duration of visits of family members and Creation of Ebola response teams in local acquaintances to Ebola isolation units and wards to 1 hour communities: Each local community should have an and effectively minimizes the strength of the detrimental Ebola response team (the grassroots movement team) traditional beliefs and customs (that aid Ebola transmis- to help educate the populace about the disease and to sion) could lead to a dramatic reduction (over 90%) of the identify potential new cases and report them to public Ebola burden in the affected communities. We note that health agencies immediately. These local teams must while the feasibility of working a 24-hour shift is a tough be well trained. Confidence-building measures, to one to operationalize, it is not unheard of in the health- help them build the trust necessary within the care profession [50]. Moreover, in situations where there communities they serve, must be embarked upon. are extreme shortages of health-care professionals during With a generally weakened health-care system in a serious crisis, as in the three countries most affected by each of the three Ebola-stricken regions [2], the time the 2014 EVD epidemic, it would not be unusual to see it takes to isolate early symptomatic cases may be health-care workers working such uncommon shifts [51]. longer. To limit such a period, and hence minimize However, it is important to note that requiring a health- underreporting, such a response team can be the ears care worker to work a 24-hour shift is physically, mentally within the local communities. However, a prompt and emotionally stressful and may result in errors and response from the health-care officials responsible for mistakes in their health-care delivery to patients [51]. In transporting these potential new cases is necessary for urgent situations and crises were this might occur, plans the response team to achieve a meaningful impact. In should be made to ensure that health-care workers who addition, the response team should serve as a support work these shifts only do so for a few days consecutively, system to the local members. Such a team should also and that the nurses and health workers working these help convince family members of the need to release shifts organize their schedules and/or patient visits so that their Ebola-deceased relatives to the trained burial they, and their colleagues, get time to rest during the teams and help them mourn properly for their loved 24-hour period (and further adequate rest at the end of ones. They can also help minimize factors relating to their shift). In other words, this study shows that the 2014 traditional/cultural beliefs and customs through Ebola outbreaks is controllable using basic public health some of the aforementioned efforts. This will also interventions (provided they are of at least a moderate- play an important role in minimizing the detrimental effectiveness level, and are implemented effectively and effect of traditional belief systems and customs. consistently). Preparedness within households: Ebola is one of those rare diseases that forbids the natural love and Recommendations care, through touch, normally provided to sick loved We conclude by providing the following list of general ones in many cultures. It is difficult for some to see recommendations, mostly directly borne out of the sim- their vulnerable loved ones sick and yet be unable to ulation results derived from this study, can help in the help. That is generally a hard concept. To avoid such Agusto et al. BMC Medicine (2015) 13:96 Page 15 of 17 circumstances, each household should have a Ebola clinics for consultation were turned down prepared outline of actions to take if symptoms of because of a lack of beds [2]). Thus, more health-care EVD become evident within the household. First, tents and units are needed for the isolation and care health-care officials should be notified. If no one from of symptomatic patients, and support in the form of the health-care system comes to transport the engineers and construction volunteers would assist in symptomatic individual to a hospital, then while the setting up such temporary and permanent health family members are still able, they should be advised facilities and tents. This would provide space for more to go to a hospital immediately, avoiding crowds. In symptomatic individuals, reducing their numbers in the case of children who may not be identified early, community settings. Moreover, health-care one responsible adult, or a parent, should be given a professionals would be needed to staff these tents. protective suit to transport the child. In the case of late symptomatic individuals, only one designated member in the household should provide support to Appendix the sick human, even though the first step should be Appendix: Formulation of the general Ebola getting all patients to the hospital or some transmission model health-care facility. This will help early detection and We use a compartmental framework to model the trans- hospitalization of cases. mission dynamics of EVD in a population stratified into Social strategy: An unspoken feature that may impact two epidemiological settings: those in the community and transmission is the social structure associated with those within the health-care system. The population of the current Ebola outbreak. Families have lost income, susceptible members of the general public (S ) is gener- schools and businesses have been disrupted and most ated at the rate  (recruitment or birth). It is further foreign-owned companies have temporarily closed increased by the return of susceptible visitors from the down, and so the day-to-day functioning and needs hospital (at a rate ρ ). The population is decreased by RV of community members have been disrupted. To help infection (at a rate λ ), natural death (at a rate μ ;this cater for the day-to-day needs of communities rate is assumed for all epidemiological compartments) and quarantined, or the potential loss of income from visits to Ebola-infected relatives in health facilities, such reduced business and cultural activities, aid should be as hospitals, clinics, make-shift tent clinics, etc. (at a rate provided to these communities (this would help ρ ). The population of exposed (latent infected) members minimize the strength of the mistrust and fear against of the community (E ) is generated at the rate λ and C C public authorities, thereby minimizing EVD cases). decreased by development of clinical symptoms of Ebola Global strategy: In each of the three Ebola-stricken (at a rate σ ), natural death (at the rate μ )and visits to C H countries, health-care workers were overwhelmed infected relatives in health facilities (at the rate ρ ). It is [52]. Health-care facilities, which were weak in the increased by the return of the visitors (at a rate ρ ). RV first place, are now even more weakened [2]. Thus The population of early infectious individuals (I )is CE support, in the form of health-care professionals, generated at the rate σ and decreased by progression from the rest of the world would help to reinforce an to the non-hospitalized symptomatic class (at a rate overwhelmed health-care system and thus help in the (1 − g)α ,where g is the fraction of these individuals fight against EVD. Given the effects long work hours who are hospitalized), hospitalization (at a rate gα ), could have on the efficiency of health-care workers, natural death and visits (at the rate ρ ). It is increased such global support would help to increase the time by the return of the visitors (at the rate ρ ). The pop- RV period between daily work shifts of health-care ulation of non-hospitalized symptomatic individuals workers who are in direct contact with ebola infected (I ) is generated at the rate (1 − g)α .Itisfurther CN C patients, there by reducing their chances of becoming increased when hospitalized members of the commu- infected, which was shown, in this study, to be an nity escape from hospital (at a rate (1 − ε)ω ;where CN effective control tool against EVD. 0 <ε ≤ 1 is the efficacy of hospitalization to prevent Furthermore, support in the form of engineers and the escape of Ebola-infected patients). This population construction volunteers is also essential. With a is decreased by recovery (at a rate γ ), hospitalization weakened health-care system in the three Ebola- (at a rate ω ) and natural death. The population of CN stricken countries [2], the time it takes to isolate early recovered members of the community (R )isgenerated symptomatic cases and move them to a health-care at a rate hγ ,where h is the fraction of non-hospitalized setting may take longer due to a lack of trained symptomatic individuals who recovered (at the rate γ ; professionals to transport the symptomatic humans, and the remaining fraction, 1 − h,isdeceased).Itis or because of a lack of beds at health-care facilities reduced by natural death. The population of members (some of the early symptomatic cases that went to of the community who died of Ebola (D ) is generated C Agusto et al. BMC Medicine (2015) 13:96 Page 16 of 17 at the rate (1 − h)γ and is decreased by cremation (at a where, rate δ ). φ β (I + I + τ I + τ D ) The equations for the dynamics of health-care workers C C CE CN C1 RH C2 C λ (I , I , I , D ) = , C CE CN RH C (those in hospitals, or health-care facilities in general, and ψ φ β (I + I + I + τ D ) health-care workers who return to the community at the H H H CEV CH H H1 H λ (I , I , I , D ) = , H CEV CH H H end of their shift) are similarly derived (and not repeated P here). with N = S + E + I + I + R + D + S + E + P C C CE CN C C RH RH S (t) =  − λ (I , I , I , D )S (t) − μ S (t) C C C CE CN RH C C H C I + R + I + R +S + E + I + S + E + RH RH CH CH V V CEV H H I ++R + D + C . H H H D −ρ S + ρ S , V C RV V E (t) = λ (I , I , I , D )S (t) − (σ + μ )E (t) C C CE CN RH C C C H C Abbreviations EBOV, Ebola virus; EVD, Ebola virus disease; PRCC, partial rank correlation −ρ E (t) + ρ E (t), V C RV V coefficient; WHO, World Health Organization. I (t) = σ E (t) − (α + μ )I (t) − ρ I (t) CE C C C H CE V CE Competing interests +ρ I (t),(4) RV CEV The authors declare that they have no competing interests. I (t) = (1 − g)α I (t) + (1 − ε)ω I (t) CN C CE CH CH Authors’ contributions −(γ + ω + μ )I (t), C CN H CN All three authors (FBA, MIT-E and ABG) participated in the model building discussion. FBA and ABG carried out the mathematical analysis and numerical R (t) = hγ I (t) − μ R (t), C C CN H C simulations. All three authors (FBA, MIT-E and ABG) participated in the writing ˙ of the manuscript. All authors read, provided updates and approved the final D (t) = (1 − h)γ I (t) − δ D (t), C C CN C C version of the manuscript. Author details S (t) =  −λ (I , I , I , D )S (t)−μ S (t) RH RH H CE CN RH C RH H RH Department of Mathematics and Statistics, Austin Peay State University, Clarksville, TN 37044, USA. Department of Mathematics, Lehigh University, −ρ S (t) + ρ S (t), Bethlehem, PA 18015, USA. Simon A. Levin Mathematical, Computational and RH RH H H Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1904, E (t) = λ (I , I , I , D )S (t)−(σ +μ )E (t) 4 RH H CE CN RH C RH H H RH USA. School of Mathematical and Natural Sciences, Arizona State University, Phoenix, AZ 85069-7100, USA. −ρ E (t) + ρ E (t), RH RH H H Received: 2 December 2014 Accepted: 10 March 2015 I (t) = σ E (t) − (γ + μ )I (t) − ω I (t), RH H RH H H RH RH RH R (t) = γ I (t) − μ R − ρ R (t) + ρ R (t), RH H RH H RH RH RH H H References 1. Centers for Disease Control and Prevention. Outbreaks chronology: Ebola virus disease. http://www.cdc.gov/vhf/ebola/outbreaks/history/ I (t) = gα I (t) + ω I (t)−[ (1 − ε)ω + γ CH C CE CN CN CN H chronology.html. Accessed 1 Feb 2015. +μ ] I (t), H CH 2. World Health Organization. Ebola virus disease, fact sheet No 103. http:// www.who.int/mediacentre/factsheets/fs103/en/. Accessed 19 Oct 2014. R (t) = f γ I (t) − μ R (t), 3. Centers for Disease Control and Prevention. Outbreaks chronology: Ebola CH H CH H CH hemorrhagic fever. http://www.cdc.gov/vhf/Ebola/resources/outbreak- table.html. Accessed 25 Aug 2014. S (t) =  − λ (I , I , I , D )S (t) − μ S (t) V V H CEV CH H H V H V 4. Centers for Disease Control and Prevention. Ebola hemorrhagic fever. http://www.cdc.gov/vhf/Ebola/. Accessed 25 Aug 2014. −ρ S (t) + ρ S (t), RV V V C 5. Ebola crisis: outbreak death toll rises to 4 447saysWHO. BBC News Africa. http://www.bbc.com/news/world-africa-29615452. Accessed 15 Oct E (t) = λ (I , I , I , D )S (t) − (σ + μ )E (t) V H CEV CH H H V V H V 6. Centers for Disease Control and Prevention. 2014 Ebola outbreak in West −ρ E (t) + ρ E (t), RV V V C Africa. http://www.cdc.gov/vhf/Ebola/outbreaks/2014-west-africa/index. html. Accessed 19 Oct 2014. I (t) = σ E (t)−μ I (t)−ρ I (t)+ρ I (t), 7. World Health Organization. Ebola situation report. http://www.who.int/ V V H RV V CEV CEV CEV CE csr/disease/ebola/situation-reports/en/. Accessed 2 Feb 2015. ˙ 8. Bray M, Chertow DS. Epidemiology and pathogenesis of Ebola virus S (t) =  − λ (I , I , I , D )S (t) − μ S (t) H H H CEV CH H H H H H disease. UpToDate. 2015. http://www.uptodate.com/contents/ −ρ S (t) + ρ S (t), H H RH RH epidemiology-and-pathogenesis-of-ebola-virus-disease?topicKey=ID %2F3023&elapsedTimeMs=1&view=print&displayedView=full. E (t) = λ (I , I , I , D )S (t) − (σ + μ )E (t) H H CE CH H H H H H H 9. Chowell G, Hengartner NW, Castillo-Chavez C, Fenimore PW, Hyman JM. The basic reproductive number of Ebola and the effects of public health −ρ E (t) + ρ E (t), H H RH RH measures: the cases of Congo and Uganda. J Math Biol. 2004;28:503–22. I (t) = σ E (t) + ω I (t) − (γ + μ )I (t), H H H RH RH H H H 10. Centers for Disease Control and Prevention. Ebola hemorrhagic fever: fact sheet. http://www.cdc.gov/vhf/Ebola/pdf/Ebola-factsheet.pdf. Accessed R (t) = f γ I (t) − μ R (t) + ρ R (t)−ρ R (t), H H H H H RH RH H H 15 Oct 2014. ˙ 11. WHO Ebola Response Team. Ebola virus disease in West Africa – the first 9 D (t) = (1 − f )γ I (t) + (1 − f )γ I (t) − δ D (t), H H CH H H H H months of the epidemic and forward projections. N Engl J Med. 2014. C (t) = δ D (t) + δ D (t), D C C H H doi:10.1056/NEJMoa1411100. Agusto et al. BMC Medicine (2015) 13:96 Page 17 of 17 12. ZMapp manufactured by MAPP Biopharmaceuticals, Inc. 6160 Lusk Blvd. # 36. Gomes MFC, Pastore Y, Piontti A, Rossi L, Chao D, Longini I, et al. C105 San Diego, CA 92121. http://www.mappbio.com/. Assessing the international spreading risk associated with the 2014 West 13. TKM Ebola manufactured by Tekmira Pharmaceuticals Corporation. 100 - African Ebola outbreakPLOS Currents Outbreaks. 2014. 8900 Glenlyon Parkway Burnaby, British Columbia Canada V5J 5J8. http:// doi:10.1371/currents.outbreaks.cd818f63d40e24aef769dda7df9e0da5. www.tekmira.com/portfolio/tkm-ebola.php. 37. Blower SM, Dowlatabadi H. Sensitivity and uncertainty analysis of 14. Ebola in West Africa, 779. Lancet Infect Dis. 2014;14:. complex models of disease transmission: an HIV model, as an example. doi:10.1016/S1473-3099(14)70785-6. Int Stat Rev. 1994;2:229–43. 15. Quist-Arction O, Poon L. How a person can recover from Ebola. 2014. 38. Marino S, Hogue I B, Ray CJ, Kirschner DE. A methodology for performing http://www.npr.org/blogs/health/2014/04/11/301464924/how-a- global uncertainty and sensitivity analysis in systems biology. J Theor Biol. patient-can-recover-from-Ebola. Accessed 25 Aug 2014. 2008;254:178–96. http://dx.doi.org/10.1016/j.jtbi.2008.04.011. 16. Althaus CL. Estimating the reproduction number of Ebola virus (EVOB) 39. McLeod RG, Brewster JF, Gumel AB, Slonowsky DA. Sensitivity and during the 2014 outbreak in West Africa. PLOS Curr Outbreaks. 2014. uncertainty analyses for a SARS model with time-varying inputs and doi:10.1371/currents.outbreaks.91afb5e0f279e7f29e7056095255b288. outputs. Math Biosci Eng. 2006;3:527–44. 17. Fasina FO, Shittu A, Lazarus D, Tomori O, Simonsen L, Viboud C, et al. 40. Guinean who brought Ebola to Senegal recovered, to return. http://www. Transmission dynamics and control of Ebola virus disease outbreak in reuters.com/article/2014/09/10/us-health-ebola-senegal- Nigeria, July to September 2014. Eurosurveillance. 2014;19:9. idUSKBN0H50V720140910. Accessed May 1, 2015. 18. Legrand J, Grais RF, Boelle PY, Valleron AJ, Flahaut A. Understanding the 41. World Health Organization. Ebola virus disease. http://www.who.int/ dynamics of Ebola epidemics. Epidemiol Infect. 2007;135:610–21. mediacentre/factsheets/fs103/en/. Accessed 29 Sep 2014. 19. Nishiura H, Chowell G. Early transmission dynamics of Ebola virus disease 42. Roy-Macaulay C. Sierra Leone quarantines two million to fight Ebola. (EVD), West Africa. Eurosurveillance. 2014;19:pii=20894. Associated Press http://news.yahoo.com/sierra-leone-cordon-off-3- 20. Towers S, Patterson-Lomba O, Castillo-Chavez C. Temporal variations in areas-stop-ebola-085631264.html. Accessed 29 Sep 2014. the effective reproduction number of the 2014 West Africa Ebola 43. Mark M. Nigeria fears fourth Ebola frontline after infected man lands in Outbreak. PLOS Curr Outbreaks. 2014. Lagos. http://www.theguardian.com/world/2014/aug/13/ebola- doi:10.1371/currents.outbreaks.9e4c4294ec8ce1adad283172b16bc908. nigerian-capital. Accessed 29 Sep 2014. 21. Meltzer MI, Atkins CY, Santibanez S, Knust B, Petersen BW, Ervin ED, 44. World Health Organization. Ebola situation in Liberia: non-conventional et al. Estimating the future number of cases in the Ebola epidemic – interventions needed. http://www.who.int/mediacentre/news/ebola/8- Liberia and Sierra Leone, 2014–2015. Morb Mortal Wkly Rep. september-2014/en/. Accessed 9 Oct 2014. 2014;63:1–14. 45. How we managed Ebola outbreak – Fashola. Daily Independent. http:// 22. Health infectious disease: health group pleads for more workers to dailyindependentnig.com/2014/09/managed-Ebola-outbreak-fashola/. combat Ebola outbreak. Time. http://time.com/3340439/Ebola-outbreak- Accessed 9 Oct 2014. west-africa-who/. Accessed 19 Oct 2014. 46. Ebola: Fashola’s impressive leadership. Leadership. http://leadership.ng/ 23. Ebola patients flee as Liberia clinic looted. Al Jazeera. http://www. columns/386173/Ebola-fasholas-impressive-leadership. Accessed 9 Oct aljazeera.com/news/africa/2014/08/Ebola-patients-flee-as-liberia-clinic- looted-201481713725590885.html. Accessed 29 Sep 2014. 47. World Health Organization. Ebola response roadmap update: 17 October 24. Hogan C. There is no such thing as Ebola. Washington Post. http://www. 2014. http://apps.who.int/iris/bitstream/10665/136645/1/ washingtonpost.com/news/morning-mix/wp/2014/07/18/there-is-no- roadmapupdate17Oct14_eng.pdf?ua=1. Accessed 18 Oct 2014. such-thing-as-Ebola/. Accessed 14 Oct 2014. 48. World Health Organization. Ebola response roadmap update: 26 25. Wilson J. Eight killed in Guinea town over Ebola fears by CNN. 2014. September 2014. http://apps.who.int/iris/bitstream/10665/135029/1/ http://www.cnn.com/2014/09/19/health/Ebola-guinea-killing/index. roadmapupdate26sept14_eng.pdf?ua=1. Accessed 29 Sep 2014. html. Accessed 29 Sep 2014. 49. World Health Organization. WHO declares end of Ebola outbreak in 26. Jerving S. Why Liberians thought Ebola was a government scam to attract Nigeria. http://www.who.int/mediacentre/news/statements/2014/ western aid. Decades of corruption have left Liberians suspicious of their nigeria-ends-ebola/en/. Accessed 20 Oct 2014. government. The Nation. http://www.thenation.com/article/181618/ 50. National Association of Neonatal Nurse Practitioners. The impact of why-liberians-thought-Ebola-was-government-scam-attract-western- advanced practice nurses’ shift length and fatigue on patient safety. 2012. aid. Accessed 14 Oct 2014. http://www.nann.org/uploads/files/Fatigue_and_APRNs.pdf. Accessed 7 27. Bloch H. Denying Ebola turns out to be a very human response. http:// Mar 2015. www.npr.org/blogs/goatsandsoda/2014/09/27/350925364/denying- 51. US Department of Labor. Extended unusual work shifts. https://www. Ebola-turns-out-to-be-a-very-human-response. Accessed 14 Oct 2014. osha.gov/OshDoc/data_Hurricane_Facts/faq_longhours.html. Accessed 28. WHO warns of West Africa’s Ebola shadow zones. Al Jazeera. http://www. 6 Mar 2015. aljazeera.com/news/africa/2014/08/who-warns-africa-Ebola-shadow- 52. Centers for Disease Control and Prevention. Non-US healthcare settings: zones-2014822225018688250.html. Accessed 9 Oct 2014. international infection control and healthcare workers. http://www.cdc. 29. Meet the world’s bravest undertakers – Liberia’s Ebola burial squad. The gov/vhf/Ebola/hcp/non-us-healthcare-settings.html. Accessed 20 Oct Telegraph. http://www.telegraph.co.uk/news/worldnews/Ebola/ 2014. 11024042/Meet-the-worlds-bravest-undertakers-Liberias-Ebola-burial- 53. Chitnis N, Cushing JM, Hyman JM. Bifurcation analysis of a mathematical squad.html. Accessed 29 Sep 2014. model for malaria transmission. SIAM J Appl Math. 2006;67:24–45. 30. World Health Organization. WHO: Ebola Response Roadmap Situation 54. Niger AM, Gumel AB. Mathematical analysis of the role of repeated Report 1 October 2014. http://apps.who.int/iris/bitstream/10665/135600/ exposure on malaria transmission dynamics. Differential Equations 1/roadmapsitrep_1Oct2014_eng.pdf. Accessed May 1, 2015. Dynamical Syst. 2008;16:251–87. 31. World Health Organization. Guinea. http://www.who.int/countries/gin/ 55. Nuño M, Reichert TA, Chowell G, Gumel AB. Protecting residential care en/. Accessed 3 Feb 2015. facilities from pandemic influenza. PNAS. 2008;105:10625–30. 32. Anderson RM, May RM. Infectious diseases of humans. Oxford: Oxford University Press; 1991. 33. Diekmann O, Heesterbeek JAP, Metz JAP. On the definition and computation of the basic reproduction ratio R in models for infectious diseases in heterogeneous populations. J Theor Biol. 1990;229:119–26. 34. Hethcote HW. The mathematics of infectious diseases. SIAM Rev. 2000;42:599–653. 35. van den Driessche P, Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci. 2002l;180:29–48.

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BMC MedicineSpringer Journals

Published: Apr 23, 2015

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