title: A renewal equation with a birth-death process as a model for parasitic infections.
abstract: 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.
authors.affiliation: Universität Tübingen, Lehrstuhl für Biomathematik, Federal Republic of Germany.
authors.forename: M
authors.initials: M
authors.lastname: Kretzschmar
mesh_terms: D000367:Age Factors; D006801:Humans; D008433:Mathematics; D015233:Models, Statistical; D010272:Parasitic Diseases / Q000453:epidemiology*; D011157:Population Dynamics