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Stability in Mathematical Biology (Wednesday, Jan. 30, 2019)

Department of Mathematics, Wilfrid Laurier University

Speaker

Professor Connell McCluskey, Department of Mathematics, Wilfrid Laurier University

Title

Stability in Mathematical Biology

Abstract

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.

Date

Wednesday, Jan. 30, 2019

Time

4 p.m. - 4:50 p.m.

Location

LH3060 (Lazaridis Hall, Room 3060)