A diffusion model for host-parasite interaction

A variety of host-parasite models are found in the literature. They usually consist of a small number of ordinary differential equations, which describe the dynamics of the total number of hosts and the total number of parasites. The authors introduced earlier a new approach to such models using a partial differential equation which uses the parasite density as a continuous structure variable. So far the new model contained only convective terms with respect to this variable, and the qualitative properties of solutions were not in agreement with observed parasite distributions. In the present work, the authors introduce diffusive terms to the previous model. Results of simulations for a specific host-parasite system appearing in fish farms are presented. These show a much better qualitative fit with real data than results from simulations with any other models.