The SIR model is one of the simplest ways to understand the spread of a disease such as COVID-19 (Coronavirus) through a population. Allowing the movement of populations makes the model slightly more realistic and results in ‘Travelling Wave’ solutions.

In this video, Oxford University Mathematician Dr Tom Crawford explains how including population migration modifies the original SIR model. He then goes on to use the results of the model to answer two important questions:

1. How fast will the disease spread?
2. How severe will the epidemic be?

The answers to these questions are discussed in the context of the current COVID-19 (Coronavirus) outbreak. The model tells us that to reduce the impact of the disease we need to lower the ‘contact ratio’ as much as possible – which is exactly what current social distancing measures are designed to do.

Watch the first video on the basic SIR model here.

Oxford University Mathematician Dr Tom Crawford explains exponential growth in the context of an epidemic such as that for COVID-19/Coronavirus. Beginning with one primary infection we see how the number of cases increases dramatically over a period of only 30 days to more than one thousand. All sources are referenced below.

The value of the reproductive number R0 = 3 is taken from current World Health Organisation estimates. Please see here for more information.

The data for the UK population is from 2018 and is sourced from Statista here.

The data for the COVID-19/Coronavirus death rate is from the Chinese Centre for Disease Control and Prevention. Please see here for more information.

The SIR model is one of the simplest disease models we have to explain the spread of a virus through a population. I first explain where the model comes from, including the assumptions that are made and how the equations are derived, before going on to use the results of the model to answer three important questions: