## Mathematical analysis of a within-host model of malaria with immune effectors and Holling type II functional response

### Volume 42 / 2015

#### Abstract

In this paper, we consider a within-host model of malaria with Holling type II functional response. The model describes the dynamics of the blood-stage of parasites and their interaction with host cells, in particular red blood cells and immune effectors. First, we obtain equilibrium points of the system. The global stability of the disease-free equilibrium point is established when the basic reproduction ratio of infection is $R_0< 1$. Then the disease is controllable and dies out. In the absence of immune effectors, when $R_0 > 1$, there exists a unique endemic equilibrium point. Global analysis of this point is given, which uses on the one hand Lyapunov functions and on the other hand results of the theory of competitive systems and stability of periodic orbits. Therefore, if $R_0 > 1$, the malaria infection persists in the host. Finally, in the presence of immune effectors, we find that the endemic equilibrium is unstable for some parameter values using the Routh–Hurwitz criterion; numerical simulations of the model also show the same results.