Absolute stability and Hopf bifurcation in a Plasmodium falciparum malaria model incorporating discrete immune response delay

We consider the absolute stability of the disease-free equilibrium of an intra-host Plasmodium falciparum malarial model allowing for antigenic variation within a single species. Antigenic variation can be viewed as an adaptation of the parasite to evade host defence [2]. The model was recently developed in [3], [4], [5] and [6]. The host’s immune response is compartmentalised into reactions to major and minor epitopes. The immune response mounted by the human host is delayed, where, for simplicity, the delay is assumed to be discrete. We investigate the resulting characteristic equation, with a view to establishing absolute stability criteria and computing the Hopf bifurcation of the disease-free equilibrium.

► We study an intra-host mathematical model of malaria caused by the Plasmodium falciparum species of parasites. ► The model incorporates the effects of delayed immune response mounted by the human host. ► The immune response delay is assumed to be discrete. ► We establish, for the first time, precise criteria for the absolute stability of the disease-free equilibrium. ► We compute, for the first time, the precise Hopf bifurcation of the disease-free equilibrium.