Mathematical Modeling and Analysis of Transmission Dynamics and Control of Schistosomiasis

Abstract

This paper presents a mathematical model that describes the transmission dynamics of schistosomiasis for humans, snails, and the free living miracidia and cercariae. The model incorporates the treated compartment and a preventive factor due to water sanitation and hygiene (WASH) for the human subpopulation. A qualitative analysis was performed to examine the invariant regions, positivity of solutions, and disease equilibrium points together with their stabilities. The basic reproduction number, $R_0$, is computed and used as a threshold value to determine the existence and stability of the equilibrium points. It is established that, under a specific condition, the disease-free equilibrium exists and there is a unique endemic equilibrium when $R_0>1$. It is shown that the disease-free equilibrium point is both locally and globally asymptotically stable provided $R_0<1$, and the unique endemic equilibrium point is locally asymptotically stable whenever $R_0>1$ using the concept of the Center Manifold Theory. A numerical simulation carried out showed that at $R_0=1$, the model exhibits a forward bifurcation which, thus, validates the analytic results. Numerical analyses of the control strategies were performed and discussed. Further, a sensitivity analysis of $R_0$ was carried out to determine the contribution of the main parameters towards the die out of the disease. Finally, the effects that these parameters have on the infected humans were numerically examined, and the results indicated that combined application of treatment and WASH will be effective in eradicating schistosomiasis.