Mathematical Model for Malaria Transmission with Optimal Control Strategies and Their Effects
Mojeeb AL-Rahman EL-Nor Osman *
School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China and Department of Mathematics and Computer Science, Faculty of Pure and Applied Sciences, International University of Africa, P.O.Box 2469, Khartoum, Sudan.
Appiagyei Ebenezer
School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China and Department of Mathematics, Valley View University, Techiman Campus, P.O.Box 183 B/A, Ghana.
Isack E. Kibona
School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we propose a SEIR-SEI optimal control model of malaria transmission with standard incidence rate. We present four control strategies to prevent the prevalence of infection in the society. In order to do this, we introduce an optimal control problem with an objective function, where the four control functions, prevention using Long-Lasting Insecticide Treated Net(LLITN) u1(t), the control effort on malaria treatment of infected individuals u2(t), the insecticide spray on the breeding grounds for the mosquito u3(t), the prevention using Indoor Residual Spraying u4(t); have been used as control measures for exposed and infected individuals. We show the existence of an optimal control pair for the optimal control problem and derive the optimality conditions. Our numerical simulation suggests that the two controls strategies u1(t)and u2(t) are more effective than the other control strategies in controlling (reducing) the number of exposed and infected individuals and also in increasing the number of recovered individuals.
Keywords: Malaria transmission, optimal control, Pontryagin’s principle, numerical simulation