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Infectious Disease Modeling

Part of the Nonlinear Systems and Complexity Book Series (volume 19)

DOI: 10.1007/978-3-319-53208-0

ISBN: 978-3-319-53206-6

Publisher: Springer International Publishing - Springer Journals

Feb 26, 2017

LitStream

Basic Theory

Liu, Xinzhi; Stechlinski, Peter

Pages: 3 –20

[Necessary mathematical definitions and concepts are presented in this chapter. Fundamental theory of ordinary differential equations is given first, followed by stability theory (including the notion of partial stability). The theory of delay differential equations, impulsive systems, and...
LitStream

Hybrid and Switched Systems

Liu, Xinzhi; Stechlinski, Peter

Pages: 21 –39

[This chapter reviews the theory of switched systems.Governed by a combination of mode-dependent continuous/discrete dynamics and logic-based switching, and having a wide range of motivating applications, the qualitative behavior of switched systems is highlighted here. Stability theory is...
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The Switched SIR Model

Liu, Xinzhi; Stechlinski, Peter

Pages: 43 –82

[The modeling of epidemics by hybrid and switched systems is introduced and analyzed. To begin, the classical SIR model is derived and its defining features are detailed. Motivated by variations in the contact rate between members of the population, a switched SIR model is formulated. The...
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Epidemic Models with Switching

Liu, Xinzhi; Stechlinski, Peter

Pages: 83 –132

[In this chapter, the methods developed thus far are applied to a variety of infectious disease models with different physiological and epidemiological assumptions. Many of the previous results are immediately applicable, thanks to the flexibility of the simple techniques used here. However, some...
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Switching Control Strategies

Liu, Xinzhi; Stechlinski, Peter

Pages: 135 –178

[This chapter is motivated by the application of control strategies to eradicate epidemics. In part, the previous switched epidemic models are reintroduced with continuous (e.g., vaccination of newborns continuously in time) or switching control (i.e., piecewise continuous application of...
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Pulse Control Strategies

Liu, Xinzhi; Stechlinski, Peter

Pages: 179 –226

[Building upon the previous chapter, impulsive control in epidemic models is formulated and analyzed in this part. Pulse vaccination, which is the control technique of applying vaccinations to a portion of the susceptible population in a relatively short time period (with respect to the dynamics...
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A Case Study: Chikungunya Outbreak in Réunion

Liu, Xinzhi; Stechlinski, Peter

Pages: 227 –257

[This chapter is devoted to analyzing the spread of the Chikungunya virus, a vector-borne disease, modeled here according to interactions between human and mosquito populations. After introducing the full model, the remainder of this chapter focuses on studying the efficacy of different control...
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Conclusions and Future Directions

Liu, Xinzhi; Stechlinski, Peter

Pages: 261 –263

[Concluding remarks are presented with a summary of contributions. Future work is also highlighted.]

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