Date/Time
Date(s) - 14/11/2024
2:30 pm - 3:30 pm

Location: Hamilton Hall, Room 410 / Zoom

Speaker: Connell McCluskey (Wilfrid Laurier University)

Title: Global Stability for Disease Models: Spotting Patterns

 Abstract: Compartment models in mathematical epidemiology are based on the idea of subdividing a population into subgroups based on epidemiological status.  One example is to divide a population into Susceptible, Exposed and Infectious, leading to an SEI model.

The long-term behaviour of such a model can sometimes be determined by finding a Lyapunov function.  Unfortunately, Lyapunov functions are notoriously difficult to find, and there is no general method for constructing them.

Despite this, over the last 20 years, there has been significant progress in finding Lyapunov functions for compartment models giving a “library” of pairs: (Differential equation,Lyapunov function)

Often, similar systems/models have similar Lyapunov functions.  When models (e.g. the SEI model) are modified in standard ways (e.g. by adding delay), the Lyapunov function seems to change in a predictable way (e.g. by requiring a particular integral term).

This suggests that the library can be used when exploring the stability of a system that is similar to another system for which a Lyapunov function is known.

In this lecture, I will discuss this process, including recent results.