Journal of Advances in Mathematics and Computer Science

Malaria is an endemic disease in many countries around the world and especially in Africa. In this paper, we developed and studied SEIR-SEI mathematical model for malaria with vertical transmission. The basic properties of the model were investigated. The next generation matrix approach was used to obtain the reproduction number, R₀, and discussed the existence of the endemic equilibrium. Furthermore, we applied four optimal control strategies to control the number of exposed and infected humans. These control strategies are: the use of treated bed nets, u₁(t); intermittent prophylactic treatment in pregnancy, u₂(t); prompt and effective case management, u₃(t), and the use of insecticide spray, u₄(t). According to our numerical simulation results, the use of all control strategies together is a very effective approach to reducing the number of exposed after some time and infected humans, while the number of recovered humans also increases. Moreover, the number of infected mosquitoes has also decreased. Thus, through these strategies together, we will be able to control the disease in a short period of time. These findings underscore the importance of timely and well-designed public health interventions in malaria outbreak scenarios.