Epidemiological Models

This chapter introduces epidemiological models as tools for analyzing the spread of infectious diseases. The focus begins with the Kermack–McKendrick SIR model, including its mathematical structure, a simplified analysis via I′/S′, and key epidemiological concepts: the basic reproduction number, the final epidemic size, and herd immunity thresholds. The discussion then extends to the SIRS model with demography, incorporating birth and death processes to study long-term persistence and endemic equilibria, supported by both analytical and numerical results. The chapter concludes with remarks on the broader role of mathematical epidemiology and a set of exercises, including extensions such as vaccination, immigration of infectious individuals, and the SLIRS model, aimed at reinforcing theoretical insights and practical modeling skills.