Global analysis of a schistosomiasis infection model with biological control

摘要

In this paper, the global stability of a schistosomiasis infection model that involves human and intermediate snail hosts as well as an additional mammalian host and a competitor snail species is studied by constructing Lyapunov functions and using properties of K monotone systems.We derive the basic reproduction number R0 for the deterministic model, and establish that the global dynamics are completely determined by the values of R0. We show that the disease can be eradicated when R0⩽1. In the case where R0>1, we prove the existence, uniqueness and global asymptotic stability of an endemic steady state. This mathematical analysis of the model gives insight about the epidemiological consequences of the introduction of a competitor resistant snail species.