A renewal equation with a birth-death process as a model for parasitic infections

A model is derived for the description of parasitic diseases on host populations with age structure. The parasite population develops according to a linear birth-death-process. The parasites influence mortality and fertility of the hosts and are acquired with a rate depending on the mean parasite load of the host population. The model consists of a system of partial differential equations with initial and boundary conditions. From the boundary condition a renewal equation for the host population is derived. The model is then generalized to describe a multitype process. Existence and uniqueness of solutions are proved. Results concerning persistent solutions are indicated.