This volume presents infectious diseases modeled mathematically, taking seasonality and changes in population behavior into account, using a switched and hybrid systems framework. The scope of coverage includes background on mathematical epidemiology, including classical formulations and results; a motivation for seasonal effects and changes in population behavior, an investigation into term-time forced epidemic models with switching parameters, and a detailed account of several different control strategies. The main goal is to study these models theoretically and to establish conditions under which eradication or persistence of the disease is guaranteed. In doing so, the long-term behavior of the models is determined through mathematical techniques from switched systems theory. Numerical simulations are also given to augment and illustrate the theoretical results and to help study the efficacy of the control schemes.

Imparts a quantitative understanding of the roles seasonality and population behavior play in the spread of a disease; Illustrates formulation and theoretical analysis of mathematical disease models and control strategies; Investigates how abrupt changes in the model parameters or function forms affect control schemes; Explains techniques from switched and hybrid systems applicable to disease models as well as many other important applications in mathematics, engineering, and computer science; Adopts a treatment accessible to individuals with a background in dynamic systems or with a background in epidemic modeling.

Autorentext

Xinzhi Liu is a Professor of Mathematics at the University of Waterloo. Peter Stechlinski is a Postdoctoral Fellow in the Process Systems Engineering Laboratory at the Massachusetts Institute of Technology

Inhalt
Introduction.- Modelling the Spread of an Infectious Disease.- Hybrid Epidemic Models.- Control Strategies for Eradication.- Discussions and Conclusions.- References.- Appendix