Mathematical Model for Malaria Disease Transmission

Abstract

Malaria is one of the fatal diseases caused by plasmodium parasites and transmitted to humans through
biting of the female of Anopheles mosquitoes. We propose a deterministic mathematical model for simulating Malaria disease transmission between humans and mosquitoes. The basic reproduction number R0 is determined by using the next-generation matrix approach. Stability conditions for the model equilibrium points with respect to R0 are derived, then we show that the forward bifurcation occurred. When R0 < 1 or R0 > 1 the Malaria disease die out or spread, respectively. The sensitivity analysis for the basic reproduction number R0 is fulfilled locally and globally. The model simulation is found by using Runge–Kutta fourth–order method in MATLAB. Furthermore, the effects of the important parameters are investigated, and we present the obtained results in graphical forms. The simulation results agree with the stability analysis for Edef are obtained. Moreover, we discuss the impacts of the Malaria disease control interventions on the important parameter for Malaria disease transmission. Finally, recommendation for control and eradicating Malaria
disease transmission is provided.