GLOBAL STABILITY OF A WITHIN-HOST DYNAMICS OF MALARIA AND THE IMMUNE SYSTEM WITH CROWLEY-MARTIN FUNCTIONAL RESPONSE
FERESHTE GAZORI *
Department of Mathematical Sciences, Sharif University of Technology, Azadi Street, Tehran, Iran.
MAHMOUD HESAARAKI
Department of Mathematical Sciences, Sharif University of Technology, Azadi Street, Tehran, Iran.
*Author to whom correspondence should be addressed.
Abstract
We consider a within-host model of malaria. This model describes the dynamics of the bloodstage of parasites and their interaction with host cells, in particular red blood cells and immune effectors. The infection rate of almost all mathematical models is linear. But in this paper, a differential equation model of malaria infection with Crowley-Martin functional response is studied. We demonstrate that if the basic reproduction number R0 < 1, the disease-free equilibrium point is globally stable and the disease dies out. In the absence of the immune effectors, when R0 > 1, a unique endemic equilibrium point is globally stable and the parasites persist in the host. Global stability of this point is illustrated by using the geometrical approach of Li and Muldwoney. In the presence of the immune effectors, the numerical analysis of the model reveals that the endemic equilibrium point can be stable or unstable.
Keywords: Within-host model of malaria, immune effectors, the basic reproduction number of infection, global stability