A SEIR-SEI Malaria Transmission Model with Optimal Control

International audience In this paper, we propose a SEIR-SEI epidemic model for malaria transmission which describes the interaction between human and mosquito population, with the effects of antibodies produced by the incidence rates for humans and mosquitoes respectively and two optimal controls. We introduce an optimal problem with an objective function, where two control functions, use of treated bed-nets and control effort on malaria treatment, have been used as control measures for infected individuals. The existence of feasible region where the model is well-known is established. Stability analysis of the disease -free equilibrium is investigated. The basic reproduction number R0; is obtained using the next generation matrix approach. The existence of the endemic equilibrium is also specified under certain conditions. Numerical simulations are carried out to confirm our analytic results and our simulation also suggests that, two control strategies are more effective than only one control in controlling the increase of number of infected individuals in the Democratic Republic of the Congo (DRC).