Mathematics Seminar - Prof. Malwina Luczak

Title: Long-term behaviour of stochastic epidemic models

Abstract:

The simplest mathematical models of epidemics are based on differential equations, and their exact and approximate solutions. Over the years, there has been increased interest in probabilistic models, which are often able to capture more accurately various aspects of the dynamics of disease spread in populations. It is relatively standard to show that, under certain conditions on the parameters and initial conditions, the variables of interest in a probabilistic model are well approximated, for a period of time, by the solution to a differential equation derived from their drift. But it can be much harder to determine to what extent such an approximation is still valid over the long-term.

In this talk, I will explore the long-term behaviour of some simple stochastic models of epidemics, and how it relates to the behaviour of the corresponding deterministic models.