Mathematical modeling of malaria disease with control strategy

Abstract

This article suggested and analyzed the transmission dynamics of malaria disease in a population using a nonlinear mathematical model. The deterministic compartmental model was examined using stability theory of differential equations. The reproduction number was obtained to be asymptotically stable conditions for the disease-free, and the endemic equilibria were determined. Moreso, the qualitatively evaluated model incorporates time-dependent variable controls which was aimed at reducing the proliferation of malaria disease. The optimal control problem was formulated using Pontryagin’s maximum principle, and three control strategies: disease prevention through bed nets, treatment and insecticides were incorporated. The optimality system was stimulated using an iterative technique of forward-backward Runge-Kutta fourth order scheme, so that the impacts of the control strategies on the infected individuals in the population can be determined. The possible influence of exploring a single control, the combination of two, and the three controls on the spread of the disease was also investigated. Numerical simulation was carried out and pertinent findings are displayed graphically.