a b s t r a c tIn 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 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 6 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.

This paper deals with the state estimation for a schistosomiasis infection dynamical model described by a continuous nonlinear system when only the infected human population is measured. The central idea is studied following two major angles. On the one hand, when all the parameters of the model are supposed to be well known, we construct a simple observer and a high-gain Luenberger observer based on a canonical controller form and conceived for the nonlinear dynamics where it is implemented. On the other hand, when the nonlinear uncertain continuous-time system is in a bounded-error context, we introduce a method for designing a guaranteed interval observer. Numerical simulations are included in order to test the behavior and the performance of the given observers.