A mathematical model is developed for a schistosomiasis infection that involves human and intermediate snail hosts as well as an additional mammalian host and a competitor snail species. The model consists of a system of eight differential equations for the infected and susceptible subpopulations. The deterministic system is generalized to a stochastic system of differential equations to account for the random behavior of demographic changes in the population levels. Values for the parameters in the model are estimated and the populations are computationally simulated under various conditions. Results of the simulations indicate several interesting features such as the rapidity by which an invading competing snail species can change the dynamics of a schistosomiasis infection.