The blood-stage dynamics of malaria infection with immune response

Abstract

This article is concerned with the dynamics of malaria infection model with diffusion and delay. The disease free threshold ${\Re }_0$ and the immune response threshold value ${\Re }_1$ of the malaria infection are obtained, which characterize the stability of the disease free equilibrium and infection equilibrium (with or without immune response). In addition, fluctuations occur when the model undergoes Hopf bifurcation as the delay passes through a certain critical value ${\tau }_0$. In this case, periodic oscillation appears near the positive steady state, which implies the recurrent attacks of disease. Finally, numerical simulations are provided to illustrate the theoretical results.

Keywords: Hopf bifurcation; Malaria; delay; diffusion; stability.