Stability analysis of a schistosomiasis model with delays

Abstract

Abstract In this work, a nonlinear deterministic model for schistosomiasis transmission including delays with two general incidence functions is considered. Rigourous mathematical analysis is done. We show that the stability of the disease-free equilibrium and the existence of an endemic equilibrium for the model are stated in terms of key thresholds parameters known as basic reproduction number R 0 . This study of the dynamic of the model is globally asymptotically stable if R 0 ≤ 1 , and the unique endemic equilibrium is globally asymptotically stable when R 0 > 1 . Some numerical simulations are provided to support the theoretical result with respect to R 0 in this paper.