A new approach to mathematical modeling of host-parasite systems

We propose a new approach to mathematical modeling of host-parasite systems by using partial differential equations where the degree of parasitism in a host is represented by a continuous variable p. This contrasts with the standard approach found in the literature of using a countable number of ordinary differential equations, one for each nonnegative integer, corresponding to the class of hosts having exactly that number of parasites. The new model bears some similarity with size-structured models of population dynamics. We specialize the model to a specific pair of helminth macroparasites infecting sea bass. We show that the model is well posed and we study its asymptotic behavior. Finally, we present results from some simulations.