Mathematical Modelling of Malaria Transmission Dynamics with Optimal Control Strategies in Kebri Dehar District, Somali Regional State, Ethiopia

Abstract

Malaria is an infectious disease caused by the Plasmodium parasite and transmitted between humans through bites of female anopheles mosquito. In this study, we present a mathematical model of malaria transmission dynamics with optimal control. We estimated the basic reproduction number for the infected cases in Kebri Dehar district from September 2011 - June 2015 E.C is . The parameters of the model are estimated by using the confirmed malaria cases of Kebri Dehar district, Ethiopia. We formulated the model for malaria and present its dynamics in details. Initially, we present the basic mathematical results and then show briefly the stability results for the model. Further, we formulate an optimal control problem with control functions and obtain the optimal control characterization. The optimal control problem is solved numerically and the results comprised of controls system for different strategies. The controls such as prevention, treatment and insecticide could use the best role in the disease eradication from the community. Our results suggest that the prevention of humans from the mosquitoes, treatment of infected humans and the insecticide spray on mosquitoes can significantly reduce the infection of malaria and may reduce further spread of infection in the community.