Mathematical Modelling of Schistosomiasis Transmission Dynamics in Traditional Cattle Farmer Communities

Abstract

In this work, a deterministic mathematical model of schistosomiasis transmission dynamics is discussed. In rural areas, many people work as a cattle farmer. Cattle farmers in endemic areas are very susceptible to schistosoma worm infection. To study the dynamics of schistosomiasis spread in traditional cattle farmer communities, we develop a mathematical model by considering human, cattle, and snail population as well as parasite density in environment. The model is expressed as a system of first order differential equations. Firstly, we verify the non-negativity and boundedness of the solutions of the model. After determining the equilibrium points of the system, we determine the basic reproduction number. Linearization and Routh Hurwitz condition are used to analyze the local stability condition of the disease free equilibrium point. Center manifold theory is used to study the local stability condition of the endemic equilibrium point. We prove global stability condition of the disease free equilibrium point by formulating suitable Lyapunov function and using LaSalle invariance principle. Several numerical simulations are presented. Our results show that the farmer should keep the cattle, water, and food clean. In addition, the farmer should use molluscicide in their farm area and give schistosomiasis drug to the cattle, regularly.