The spread of a parasitic infection in a spatially distributed host population

Starting from a stochastic model for the spread of a parasitic infection in a spatially distributed host population we describe the way to a continuum formulation by a deterministic model in terms of a nonlinear partial differential equation and an integro-differential equation. The hosts are assumed to occupy fixed spatial positions, whereas the parasites are mobile, however can propagate only within the hosts. To perform the continuum limit we suppose that the size N_hof the host population, the size N_pof the parasite population, and the ratio N_p/N_htend to infinity. Accordingly, the parameters determining the time evolution of the host and parasite populations are rescaled suitably.Parts of this work have been elaborated during a stay at the Institute of Applied Mathematics at the University of Zürich