Optimal control analysis of schistosomiasis dynamics

Abstract

This paper presents an extension of a deterministic epidemic model for schistosomiasis. The model is extended into an optimal control problem with the inclusion of three time-dependent optimal control measures. The optimal controls included are: early diagnosis and treatment of exposed humans; snail elimination using chemical mulluscicide; and chlorination of water to eliminate free living cercariae. The existence of the optimal control solution is proven and the necessary conditions required for an optimal control with respect to the proposed model was established using Pontryagin’s minimum principle. The forward-backward Runge Kutta scheme was used to carry out the numerical simulation. Seven control measures (S1–S7) were simulated using the three control strategies: u1(t), u2(t) and u3(t) and a combination of these controls. The results from the numerical simulation showed the effectiveness of each of the control strategies in controlling the prevalence of schistosomiasis. Based on the results, the most effective and swift control strategies are those involving snail elimination using chemical mulluscicide. But due to the environmental implications of these control strategies, as it may lead to total extinction of the snails, it is highly recommended that no control involving snail elimination should be practiced. Thus, the best and also an effective control strategy will be a combination of treatment of infectious individuals and water treatment to eliminate cercariae by chlorination.