Stability analysis of a schistosomiasis model with delays

---

Résumé

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 R0 . This study of the dynamic of the model is globally asymptotically stable if R0≤1 , and the unique endemic equilibrium is globally asymptotically stable when R0>1 . Some numerical simulations are provided to support the theoretical result with respect to R0 in this paper.

Mots-clés

schistosomiasis transmission, time delay, basic reproduction number, disease-free equilibrium, endemic equilibrium, global asymptotic stability, nonlinear epidemic model