# Lois Veen: The SIR Model: Understanding the Spread of Disease

BsC Project

**Time: **
Fri 2020-04-03 11.00 - 12.00

**Lecturer: **
Lois Veen

**Location: **
Zoom, Meeting ID: 167 895 497

**Supervisor: **
Yishao Zhou

### Abstract

The SIR (Susceptible-Infected-Recovered) model is an epidemiological model used to estimate the spread of infectious diseases. This paper aims to provide the reader with a description of the model and it’s applications, using both mathematical theory and real world data. The first part gives some contextual background and explains the mathematics behind the model. Numerical

solutions to the model are then discussed using the methods of Euler and Runge-Kutta. This is followed by a qualitative analysis of the model, where concepts such as epidemic threshold, equilibrium, and epidemic size are investigated. We then study ways of analyzing the effects of vaccination and explain how the World Health Organization (WHO) in 1980 managed to eradicate smallpox. In the last part of this paper we use the newly collected data on COVID-19 to estimate the disease’s basic reproduction number R0, as well as to investigate the effects of public health measures.