An optimal control of malaria transmission model with mosquito seasonal factor

Abstract

Malaria is an infectious disease which causes a global health problem. This paper aims to construct and analyze a malaria model with a seasonal factor and also apply optimal control variables in the form of insecticide, prevention, and treatment. The malaria model without seasonal factor has two equilibria, namely, the disease-free equilibrium (DFE) and the endemic equilibrium (EE). The existence and local stability of the equilibria depend on the basic reproduction number. We further analyze the sensitivity of the parameters to determine which parameters are the most influential in the model. Then, the malaria model by considering a seasonal factor is presented. The simulation results indicate that the seasonal factor tends to be more influential on the dynamics of the infected mosquitoes and humans population in region with hot climate. Furthermore, the existence of the optimal control variable in the malaria model with seasonal factor is determined through the Pontryagin Maximum Principle. Numerical simulation of the model with the optimal control shows that providing controls in the form of insecticide, prevention, and treatment simultaneously are effective in reducing the number of the exposed and infectious of the human population and also the infectious mosquito population.