Mathematical Modelling and Optimal Control of Malaria Using Awareness-Based Interventions

Abstract

Malaria is a critical fevered illness caused by Plasmodium parasites transmitted among people through the bites of infected female Anopheles mosquitoes. Public awareness about the disease is important for the control of disease. This article proposes a mathematical model to study the dynamics of malaria disease transmission with the influence of awareness-based control interventions. We found two equilibria of the model, namely the disease-free and endemic equilibrium. Disease-free equilibrium is stable globally if basic reproduction number (R0) is less than unity (R0<1). Some basic mathematical properties of the proposed model, such as nonnegativity and boundedness of solutions, the feasibility of the equilibrium points and their stability properties, have been studied. Finally, we adopted optimal control to minimize the cost of disease control and solve the problem by formulating Hamiltonian functional. The optimal use of insecticides for controlling the mosquito population is determined. Numerical simulations have been provided for the confirmation of the analytical results. We conclude that media awareness with optimal control approach is best for cost-effective malaria disease management.