Global analysis of a schistosomiasis infection model with biological control
Abstract
In this paper, the global stability of a schistosomiasis infection model that involves human and intermediate snail hosts as well as an additional mam-malian host and a competitor snail species is studied by constructing Lya-punov functions and using properties of K monotone systems. We derive the basic reproduction number R 0 for the deterministic model, and establish that the global dynamics are completely determined by the values of R 0 . We show that the disease can be eradicated when R 0 ≤ 1. In the case where R 0 > 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.
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