Global analysis of a reaction–diffusion blood-stage malaria model with immune response

Abstract

Malaria is one of the most dangerous diseases that threatens people’s lives around the world. In this paper, we study a reaction-diffusion model for the within-host dynamics of malaria infection with an antibody immune response. The model is given by a system of partial differential equations (PDEs) to describe the blood-stage of malaria life cycle. It addresses the interactions between uninfected red blood cells, antibodies, and three types of infected red blood cells, namely ring-infected red blood cells, trophozoite-infected red blood cells and schizont-infected red blood cells. Moreover, the model contains a parameter to measure the efficacy of isoleucine starvation and its effect on the growth of malaria parasites. We show the basic properties of the model. We compute all equilibria and derive the thresholds from the conditions of existence of malaria equilibrium points. We prove the global stability of all equilibrium points based on choosing suitable Lyapunov functionals. We use the characteristic equations to verify the local instability of equilibrium points. We finally execute numerical simulations to validate the theoretical results and highlight some important observations. The results indicate that isoleucine starvation can have a critical impact on the stability of equilibrium points. When the efficacy of isoleucine starvation is high, it switches the system from the infection state to the malaria-free state. The presence of an antibody immune response does not lead to the elimination of malaria infection, but it suppresses the growth of malaria parasites and increases the amount of healthy red blood cells.