Department of Mathematics Seminar
Speaker: Professor Connell McCluskey, Department of Mathematics, Wilfrid Laurier University
Title: Stability in Mathematical Biology
In the 1920's, Alfred Lotka and Vito Volterra (working separately) developed the same mathematical model of a predator-prey system. The solutions of this system are periodic and can be graphed as closed loops in the xy-plane. This can be shown by using a simple function g(x) = x - 1 - ln(x).
In the early 2000's, the same function was used to study 2- and 3-dimensional models of disease spread – this time showing that solutions were not periodic. Instead, it was shown that solutions would tend to a constant value called an equilibrium. We say that the equilibrium is globally asymptotically stable.
A few years later, the same function was used to show that higher dimensional disease models had a globally asymptotically stable equilibrium. More recently, it was used for infinite dimensional disease models.
I will give an introduction to this area, including some recent projects that students at Laurier have worked on.