# Epidemiological Models with Seasonality

Chapter
Part of the Lecture Notes on Mathematical Modelling in the Life Sciences book series (LMML)

## Abstract

Epidemiology is the branch of medicine that deals with incidence, distribution, and control of diseases in a population. At the basic level the population is divided into susceptible, exposed, infected, and recovered compartments. However, often infection is caused not only by exposed or infected individuals but also by other species, such as mosquitos in the case of malaria, or waste water in the case of cholera. In attempting to model the transmission of the disease one has to take into account the facts that infection rates may vary among different populations (due, for instance, to those who underwent vaccination and those who did not), as well as from one season to another. In this chapter we focus on seasonality-dependent diseases and ask the question whether initial infection of one or a small number of individuals will cause the disease to spread or whether the disease will die out. To answer this question we invoke the concept of the basic reproduction number, a number which is easy to compute in the case of seasonality-independent diseases, but difficult to compute in the case of diseases with seasonality.

### Keywords

Hepatitis Tuberculosis Diarrhea Malaria Cholera

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