The Within-Host dynamics of malaria infection with immune response - Yilong Li; Shigui Ruan; Dongmei Xiao (Mathematical Biosciences and Engineering, 2011)
Malaria infection is one of the most serious global healthproblems of our time. In this article the blood-stage dynamics ofmalaria in an infected host are studied by incorporating red bloodcells, malaria parasitemia and immune effectors into a mathematicalmodel with nonlinear bounded Michaelis-Menten-Monod functionsdescribing how immune cells interact with infected red blood cellsand merozoites. By a theoretical analysis of this model, we show thatthere exists a threshold value $R_0$, namely the basic reproduction number,for the malaria infection. The malaria-free equilibrium is global asymptoticallystable if $R_01$, there exist two kinds ofinfection equilibria: malaria infection equilibrium (withoutspecific immune response) and positive equilibrium (with specificimmune response). Conditions on the existence and stability of bothinfection equilibria are given. Moreover, it has been showedthat the model can undergo Hopf bifurcation at thepositive equilibrium and exhibit periodic oscillations. Numericalsimulations are also provided to demonstrate these theoreticalresults.