Introduction to Epidemic Modeling

Abstract

This chapter is the introductory chapter to epidemiological modeling. The chapter starts with the derivation of the Kermack–McKendrick SIR ODE epidemic model. Furthermore, it studies the basic mathematical properties of the model. The model is then fitted to data on influenza at an English boarding school, and its parameters are estimated from the data. In addition, a simple SIS model is introduced and reduced to a single-equation epidemic model. General techniques for studying the dynamics of single-equation ODE models are described and applied to the single-equation version of the SIS model. Furthermore, the SIS model is extended to an SIS model with saturating treatment. The analysis of the model with saturating treatment leads to the introduction of the concepts of multiple equilibria and bistability.