Oscillations in an Intra-host Model of <Emphasis Type="Italic">Plasmodium Falciparum</Emphasis> Malaria Due to Cross-reactive Immune Response

We consider an intra-host model of malaria that allows for antigenic variation within a single species. More specifically, the host’s immune response is compartmentalized into reactions to major and minor epitopes. We investigate the conditions that lead to transient oscillations, which correspond to recurrent clinical episodes of the diseases, and how a small delay in the activation of the immune response can lead to persistent oscillations. We find that the efficacies of the immune responses to the major and minor epitopes, defined in terms of rate constants, play a crucial role in determining when there will be transient oscillations. The delay necessary to excite persistent oscillations, the time duration between disease episodes and their severity are also expressed in terms of the immune response efficacies. In addition, we describe how the severity and duration of the oscillations depend upon the parasite propagation rates and the immune response efficacies.