Existence and uniqueness of solutions for a diffusion model of host–parasite dynamics

Milner and Patton (J. Comput. Appl. Math., in press) introduced earlier a new approach to modeling host–parasite dynamics through a convection–diffusion partial differential equation, which uses the parasite density as a continuous structure variable. A motivation for the model was presented there, as well as results from numerical simulations and comparisons with those from other models. However, no proof of existence or uniqueness of solutions to the new model proposed was included there. In the present work the authors deal with the well posedness of that model and they prove existence and uniqueness of solutions, as well as establishing some asymptotic results.  2003 Elsevier Science (USA). All rights reserved.