Abstract
This chapter introduces and studies discrete epidemic modeling. The chapter begins with single species discrete models of population growth. Tools for the analysis of single equation discrete models are introduced and applied to the population models. The concepts of 2-cycle, 4-cycle, and period doubling are introduced and illustrated. The chapter includes the mathematical tools for studying higher dimensional models, such as Jury conditions. It then applied these tools to study a discrete SIS and a discrete SEIS epidemic models. A generalization of the next-generation approach to discrete models is given and applied to the computation of the reproduction number of the SEIS and a two-patch SIS models. The chapter concludes with the introduction and analysis of a discrete SARS epidemic model.
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