A simple model for the within-host dynamics of a protozoan parasite.

The dynamics of parasite-host systems can be complicated if the parasite life cycle contains an obligatory environmental stage and if the hosts' immunity increases upon re-infection. The dynamics then greatly depend on the relation between infection history and parasite uptake and excretion of individual hosts. In an effort to better understand such systems, we study Eimeria spp. in chickens as our model. In this paper we take a first step and study the within-host dynamics of Eimeria spp. transmitted through oocysts in the environment, with a mathematical model for the parasite life cycle in discrete time, interacting with a single variable describing the immune response. The model can explain various types of oocyst input-output behaviour as described in previous experiments, in particular the characteristic crowding effect, which causes a decreasing oocyst production with increasing single dose oocyst uptake. Oocyst excretion during constant oocyst uptake (trickle infection) and the immunizing effect of single and trickle infections also appears in accordance with published experiments. The model seems a good description of oocyst input-output behaviour in individual hosts; it provides a solid basis for the study of between-host dynamics, where individuals interact in a common environment, thereby affecting their own and each other's infection pattern.