The epidemic models

When we want to describe how a pathogen or a disease is spread into a population, we need to create a model using mathematical, statistical, or computational tools. The most common model used in the epidemiology is SIR (susceptible, infected, and recovered) model, which was formulated in the paper A Contribution to the Mathematical Theory of Epidemics by McKendrick and Kermack published in 1927.

In the models presented in this chapter, we assume a closed population (without births or deaths) and that the demographics and socio-economic variables do not affect the spread of the disease.

The SIR model

The SIR epidemiological model describes the course of an infectious disease, as we can see in the following figure. Starting with a susceptible population (S), which comes into contact with an infected population (I), where the individual remains infected and once the infection period has passed, the individual is then in the recovered state (R):

In this chapter we will use two...