Maths Project Repository Database

The dynamics of infectious disease transmission are often modelled using a system of ordinary differential equations. An important summary quantity that can be calculated for this kind of model is the basic reproduction number, $R_0$. This is defined as the average number of onward infections that a typical infected individual produces, and an infection can invade a population if and only if $R_0$ is greater than 1. It often happens that there is variation in contact rates, e.g. for insect-borne infections, some people are bitten much more than others. This project would first review how $R_0$ is calculated in the general case, and then how variation in contact rates changes $R_0$. The student may implement one or more types of model to numerically verify the behaviour.