Mathematical Analysis and Optimal Control of Schistosomiasis Transmission Model

Abstract

Schistosomiasis, a health challenge in many communities, is prevalent as the rate of infection is one in every thirty individuals. In this work, a deterministic model for schistosomiasis transmission dynamics is studied. The stability properties of equilibrium states, disease-free and endemic equilibria are established in terms of the basic reproduction number, R_0. The sensitivity analysis of R_0 with respect to the model parameters is carried out using Partial rank correlation coefficients (PRCCs). The optimal control model with control measures, public health education, diagnosis and treatment and snail control, is formulated and its optimality system is derived using Pontragyin's maximum Principle. Simulation results showed that simultaneous implementation of public health education, diagnosis and treatment and snail control will reduce the burden of the schistosomiasis infection in the population. However due to toxicity of some snail controls to other aquatic bodies and difficulty to single out the chemical control that will focus only on the snail population even though snails are special food in Africa, it is preferable to implement public health education and diagnosis and treatment simultaneously in order to eradicate schistosomiasis transmission in the affected regions.