Analysis Of Malaria Infection Dynamic Models

In this paper, mathematical models are proposed for Plasmodium falciparum infection in blood-stage. Considering the saturated infection incidences and the effect of immune satura-tion, we develop a mathematical model of malaria with two competitive strains of Plasmodium falciparum and a malaria dynamic model with Beddington-DeAngelis functional response. The dynamic properties with their biological meanings are studied. Background knowledge about malaria, progress of malaria dynamics and some basic theory are introduced in Chapter 1.In Chapter 2, saturated infection incidences and immune responses are incorporated into a mathematical model of malaria with two competitive strains of Plasmodium falciparum. The basic reproductive numbers of pathogens and the response numbers of host immunity are for-mulated. The complete classifications of global stability of the model are established in terms of these numbers by using the persistence theory and Lyapunov methods. It is found that two strains of parasites coexist within a host when the reproductive numbers and responsive numbers satisfy the explicit conditions defined by two inequalities, and undergo the competitive exclusion otherwise. This means that the introduction of saturated infection rates induces the coexistence. By numerical simulations, we see that the immune responses can dramatically reduce malaria infections.In Chapter 3, a malaria dynamic model with Beddington-DeAngelis functional response is proposed. By the next generation matrix method, the basic reproduction number Ro can be obtained. By constructing Lyapunov functions, it is shown that the infection-free equilibrium is globally asymptotically stable when R0<1 and the positive equilibrium is globally asymptoti-cally stable when R0>1.