Development and analysis of a mathematical model for the life cycle of schistosomiasis

Schistosomiasis is a helminth infection with an intermediate host (snails) and a definitive host (man). This paper presents a mathematical model for the life cycle of schistosomiasis. The continuous model consists of a system of three ordinary differential equations. Existence of limit cycles, stability of equilibrium, and persistence for two cases of the general model are presented. Numerical solutions to these two cases, plus, numerical solutions to a third case, not geometrically solveable, are also presented.

The general system is found to have no limit cycles, or cycle graphs, in the population quadrant. There is a breakpoint and a threshhold value for the mean number of worms per human host (for fixed numbers of healthy and infected snails). A globally stable, positive unique equilibrium exists for the healthy and infected snail populations for a constant infectivity rate.