Mathematical model of schistosomiasis with health education and molluscicide intervention

Abstract

In this article, a mathematical model is developed to study the impact of health education and molluscicide intervention on the spread of schistosomiasis. The model constructed consists of seven ordinary differential equations that describe susceptible human, latent human, infectious human, susceptible snail, infected snail, miracidia and cercarie. After analyzing non-negativity and boundedness of solutions of the model, we determine the disease free equilibrium point and the endemic equilibrium point as well as their existence conditions. The basic reproduction number is determined using the next generation matrix approach. The local stability condition of the disease-free equilibrium point is proved by using linearization and Descartes’ sign rule.. The Center Manifold Theory is used to prove the local stability condition of the endemic equilibrium point and to identify the existence of bifurcation. We constructed Lyapunov function to show that the disease-free equilibrium point is globally asymptotically stable under sufficient condition. We present numerical simulations to support our theoretical study. Numerical simulations show that health education and molluscicide intervention are able to reduce schistosomiasis cases in human and snail populations. Molluscicide intervention is a very effective method to control the spread of schistosomiasis.