Immune response to a malaria infection: properties of a mathematical model

We establish some properties of a within host mathematical model of malaria proposed by Recker et al. [M. Recker et al., Transient cross-reactive immune responses can orchestrate antigenic variation in malaria, Lett. Nature 429 (2004), pp. 555-558; M. Recker and S. Gupta, Conflicting immune responses can prolong the length of infection in Plasmodium falciparum malaria, Bull. Math. Biol. 68 (2006), pp. 821-835.], which includes the role of the immune system during the infection. The model accounts for the antigenic variation exhibited by the malaria parasite (Plasmodium falciparum). We show that the model can exhibit a wide variety of dynamical behaviours. We provide criteria for global stability, competitive exclusion and persistence. We also demonstrate that the disease equilibrium can be destabilized by non-symmetric cross-reactive responses.