February 2, 2012
Title: Bifurcation, Stability, and Cluster Formation ofMulti-Strain Infection Models
Abstract: Clustering behaviours have been found in numerous ODE based multi-strain epidemiological models. Numerical solutions of these models have shown that steady-states, periodic, or even chaotic motions can be self-organized into clusters. Such clustering behaviours are not a priori expected. It has been proposed that the cross-protection from multiple strains of pathogens is responsible for the clustering phenomenon. In this talk, I will show that the steady-state clusterings in existing models can be analytically predicted. The clusterings occur via semi-simple double zero bifurcations from the quotient networks of the models and the patterns which follow can be predicted through the stability analysis of the bifurcation. Finally, the biological implications of these results are discussed.