Hopf bifurcation in epidemiological models with delays

Abstract

Epidemiological models with time delays often display oscillations, this thesis will present the conditions needed for either stable or unstable periodic solutions to occur within these models. We will specifically look at models for which the stability changes as a function of the time delay and provide formulas to determine the stability of periodic cycles. Then we will analyse some specific models using the MATLAB package DDE-BIFTOOL.