Synchrony-Breaking Hopf bifurcation in a Model of antigenic variation

In this paper, we will analyze the bifurcation dynamics of an in vivo model of Plasmodium falciparum. The main attention of this model is focused on the dynamics of cross-reactivity from antigenic variation. We apply the techniques of coupled cell systems to study this model. It is shown that synchrony-breaking Hopf bifurcation occurs from a nontrivial synchronous equilibrium. In proving the existence of a Hopf bifurcation, we also discover the condition under which possible 2-color synchrony patterns arise from the bifurcation. The dynamics resulting from the bifurcation are qualitatively similar to known behavior of antigenic variation. These results are discussed and illustrated with specific examples and numerical simulations.