A schistosomiasis model with mating structure and time delay

A system of homogeneous equations with a time delay is used to model the population dynamics of schistosomes. The model includes the parasite's mating structure, multiple resistant schistosome strains, and biological complexity associated with the parasite's life cycle. Invasion criteria of resistant strains and coexistence threshold conditions are derived. These results are used to explore the impact of drug treatment on resistant strain survival. Numerical simulations indicate that the dynamical behaviors of the current model are not qualitatively different from those derived from an earlier model that ignores the impact of time delays associated with the multiple stages in parasite's life cycle. However, quantitatively the time delays make it more likely for drug-resistant strains to invade in a parasite population.