Global analysis of a mathematical model on malaria with competitive strains and immune responses

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 formulated. 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.