Asymptotic analysis of schistosomiasis persistence in models with general functions

A general mathematical model for schistosomiasis is formulated that incorporates the miracidia and cercariae dynamics, since parasites play an important role in the transmission dynamics of schistosomiasis. Under the biologically motivated assumptions, the basic reproduction number R0 is defined and shown to give a sharp threshold that determines whether or not the disease dies out. By using Lyapunov functions, we conclude that if R0<1, then the disease-free equilibrium is globally asymptotically stable, and schistosomiasis dies out; if R0>1, then the disease-free equilibrium is unstable, a unique endemic equilibrium is globally asymptotically stable, and schistosomiasis persists at a positive level.