Applied Mathematics Seminar | Pei Yu, Modelling and Dynamical Analysis of Recurrent Infections

In this talk, we will present dynamic models of recurrent infections in individuals. These viral infections, HIV being a well-known example, have long periods of low viral activity punctuated by episodes of high viral reproduction. Previous models of the dynamics of these viral blips used either stochastic components or forcing terms as the triggers to simulate the phenomenon. Our new developed models require neither stochastic features nor forcing terms and generate the viral blips by dynamic bifurcations. Using dynamical systems theory, we hypothesize the conditions for the existence of viral blips in a deterministic in-host infection model. These conditions allow us to develop very simple (2- and 3-dimensional) infection models which produce viral blips, and we determine the complete parameter range for the 3-dimensional model in which blips are possible, using stability and bifurcation analysis. We will also discuss the relation of our approach with the singular perturbation method as well as their differences.