Access the full text.
Sign up today, get DeepDyve free for 14 days.
T. Moon (1976)
A statistical model of the dynamics of a mosquito vector (Culex tarsalis) population.Biometrics, 32 2
J. Charlwood, R. Thompson, H. Madsen (2003)
Observations on the swarming and mating behaviour of Anopheles funestus from southern MozambiqueMalaria Journal, 2
R. Costantino, R. Desharnais, J. Cushing, B. Dennis (1997)
Chaotic Dynamics in an Insect PopulationScience, 275
M. Klowden (2001)
Sexual receptivity in Anopheles gambiae mosquitoes: absence of control by male accessory gland substances.Journal of insect physiology, 47 7
P. Verhulst
Notice sur la loi que la population suit dans son accroissement. Correspondance Mathematique et Physique Publiee par A, 10
B. Yuval, G. Fritz (1994)
Multiple mating in female mosquitoes—evidence from a field population of Anopheles freeborni (Diptera: Culicidae)Bulletin of Entomological Research, 84
G. Ngwa, William Shu (2000)
A mathematical model for endemic malaria with variable human and mosquito populationsMathematical and Computer Modelling, 32
W Hahn (1967)
Stabilty of motion
T. Porphyre, D. Bicout, P. Sabatier (2005)
Modelling the abundance of mosquito vectors versus flooding dynamicsEcological Modelling, 183
A. Lutambi, M. Penny, T. Smith, N. Chitnis (2013)
Mathematical modelling of mosquito dispersal in a heterogeneous environment.Mathematical biosciences, 241 2
S. Jang (2005)
Contest and scramble competition with a dynamic resourceNonlinear Analysis-theory Methods & Applications, 63
Martin Eichner (1996)
Difference equation model for malaria transmission and disease
Ian Hastings, Umberto D'Alessandro (2000)
Modelling a predictable disaster: the rise and spread of drug-resistantmalaria.Parasitology today, 16 8
JD Charlwood, MDR Jones (1979)
Mating behaviour in the mosquito Anopheles gambiae s. l. i. Close range and contact behaviourPhysiol Entomol, 4
J. Smith, M. Slatkin (1973)
The Stability of Predator‐Prey SystemsEcology, 54
L. Gomulski (1990)
Polyandry in nulliparous Anopheles gambiae mosquitoes (Diptera: Culicidae)Bulletin of Entomological Research, 80
W. Takken, B. Knols (1999)
Odor-mediated behavior of Afrotropical malaria mosquitoes.Annual review of entomology, 44
G. Ngwa (2006)
On the Population Dynamics of the Malaria VectorBulletin of Mathematical Biology, 68
L. Baton, L. Ranford-Cartwright (2005)
Spreading the seeds of million-murdering death: metamorphoses of malaria in the mosquito.Trends in parasitology, 21 12
C. Ngonghala, M. Teboh-Ewungkem, G. Ngwa (2014)
Persistent oscillations and backward bifurcation in a malaria model with varying human and mosquito populations: implications for controlJournal of Mathematical Biology, 70
M. Teboh-Ewungkem, G. Ngwa, C. Ngonghala (2013)
Models and Proposals for Malaria: A ReviewMathematical Population Studies, 20
J. Silvester (2000)
Determinants of block matricesThe Mathematical Gazette, 84
S. Levin (1983)
Lectu re Notes in Biomathematics
PF Verhulst (1838)
Notice sur la loi que la population suit dans son acroissementCorr Math Phys, 10
Siewe Nourridine, M. Teboh-Ewungkem, G. Ngwa (2011)
A mathematical model of the population dynamics of disease-transmitting vectors with spatial considerationJournal of Biological Dynamics, 5
C. Villarreal, G. Fuentes-Maldonado, M. Rodríguez, B. Yuval (1994)
Low rates of multiple fertilization in parous Anopheles albimanus.Journal of the American Mosquito Control Association, 10 1
M. Teboh-Ewungkem, T. Yuster (2010)
A within-vector mathematical model of Plasmodium falciparum and implications of incomplete fertilization on optimal gametocyte sex ratio.Journal of theoretical biology, 264 2
G. Ngwa, Ashrafi Niger, A. Gumel (2010)
Mathematical assessment of the role of non-linear birth and maturation delay in the population dynamics of the malaria vectorAppl. Math. Comput., 217
J. Charlwood, M. Jones (1979)
Mating behaviour in the mosquito, Anopheles gambiae s.1.savePhysiological Entomology, 4
S. Wanji, F. Mafo, N. Tendongfor, M. Tanga, E. Tchuente, C. Bilong, T. Njiné (2009)
Spatial distribution, environmental and physicochemical characterization of Anopheles breeding sites in the Mount Cameroon region.Journal of vector borne diseases, 46 1
M. Teboh-Ewungkem, Miao Wang (2012)
Male fecundity and optimal gametocyte sex ratios for Plasmodium falciparum during incomplete fertilization.Journal of theoretical biology, 307
James Powell, Jesse Logan (2005)
Insect seasonality: circle map analysis of temperature-driven life cycles.Theoretical population biology, 67 3
H. Gilles, D. Warrell (1993)
Bruce-Chwatt's essential malariology.
O. Diekmann, J. Heesterbeek, J. Metz (1990)
On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populationsJournal of Mathematical Biology, 28
P. Driessche, James Watmough (2002)
Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission.Mathematical biosciences, 180
C. Ngonghala, G. Ngwa, M. Teboh-Ewungkem (2012)
Periodic oscillations and backward bifurcation in a model for the dynamics of malaria transmission.Mathematical biosciences, 240 1
J. Silver (2008)
Mosquito Ecology: Field Sampling Methods
I. Nåsell (1985)
Hybrid Models of Tropical Infections
Ingemar Nåsell (1985)
Hybrid models of tropical infections. Lecture notes in biomathematics
L. Takahashi, Norberto Maidana, W. Ferreira, P. Pulino, H. Yang (2005)
Mathematical models for the Aedes aegypti dispersal dynamics: Travelling waves by wing and windBulletin of Mathematical Biology, 67
Philip McCall, D. Kelly (2002)
Learning and memory in disease vectors.Trends in parasitology, 18 10
B. Yandell, D. Hogg (1988)
Modelling insect natality using splinesMathematical and Computer Modelling, 12
M. Castañera, J. Aparicio, R. Gürtler (2003)
A stage-structured stochastic model of the population dynamics of Triatoma infestans, the main vector of Chagas diseaseEcological Modelling, 162
Å. Brännström, D. Sumpter (2005)
The role of competition and clustering in population dynamicsProceedings of the Royal Society B: Biological Sciences, 272
M. Raffy, A. Tran (2005)
On the dynamics of flying insects populations controlled by large scale information.Theoretical population biology, 68 2
M. Klowden, H. Briegel (1994)
Mosquito gonotrophic cycle and multiple feeding potential: contrasts between Anopheles and Aedes (Diptera: Culicidae).Journal of medical entomology, 31 4
N. Chitnis, J. Cushing, J. Hyman (2006)
Bifurcation Analysis of a Mathematical Model for Malaria TransmissionSIAM J. Appl. Math., 67
O Diekmann, JAP Heesterbeek, JAJ Metz (1990)
On the definition and the computation of the basic reproduction ratio $${R}_0$$ R 0 in models for infectious diseases in heterogeneous populationsJ Math Biol, 28
N. Parke, W. Kaplan (1958)
Ordinary Differential Equations.American Mathematical Monthly, 67
G. Craig (1967)
Mosquitoes: Female Monogamy Induced by Male Accessory Gland SubstanceScience, 156
A reproductive stage-structured deterministic differential equation model for the population dynamics of the human malaria vector is derived and analysed. The model captures the gonotrophic and behavioural life characteristics of the female Anopheles sp. mosquito and takes into consideration the fact that for the purposes of reproduction, the female Anopheles sp. mosquito must visit and bite humans (or animals) to harvest necessary proteins from blood that it needs for the development of its eggs. Focusing on mosquitoes that feed exclusively on humans, our results indicate the existence of a threshold parameter, the vectorial reproduction number, whose size increases with increasing number of gonotrophic cycles, and is also affected by the female mosquito’s birth rate, its attraction and visitation rate to human residences, and its contact rate with humans. A stability analysis of the model indicates that the mosquito can establish itself in the environment if and only if the value of the vectorial reproduction number exceeds unity and that mosquito eradication is possible if the vectorial reproduction number is less than unity, since, then, the trivial steady state which always exist is unique and is globally and asymptotically stable. When a persistent vector population steady state exists, it is locally and asymptotically stable for a range of reproduction numbers, but can also be driven to instability via a Hopf bifurcation as the reproduction number increases further away from unity. The model derivation identifies and characterizes control parameters relating to activities such as human-mosquito contact and the mosquito’s survival chances between blood meals and egg laying. Our results show that the total mosquito population size increases with increasing number of gonotrophic cycles. Therefore understanding the fundamental aspects of the mosquito’s behaviour provides a pathway for the study of human-mosquito contact and mosquito population control. Control of the mosquito population densities would ultimately lead to malaria control.
Bulletin of Mathematical Biology – Springer Journals
Published: Sep 19, 2014
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.