Mathematical modeling of malaria with vaccination, treatment and vector control

Malaria is an infectious disease caused by the Plasmodium parasite, and transmitted amongst humans through the bites of the female Anopheles mosquito. In this work, we used a system of nonlinear ordinary differential equations to model the disease. The new model incorporated vaccination, treatment and vector control using sterile-insect technology (SIT). Through stability analysis, we showed that the malaria-free equilibrium (MFE) point is locally and globally asymptotically stable (GAS) when the malaria control number, [Formula: see text] is less than one, and unstable otherwise. The global stability of the MFE is an indication that there exists a unique endemic equilibrium point in the system and the absence of backward bifurcation in the model. The existence of the endemic equilibrium is shown and seen to be GAS. The work also showed the effects of treatment, vaccination and vector control in controlling malaria. Also, sensitivity analysis of important model parameters were shown. The result showed that effective treatment of infectious humans with malaria helps to reduce the spread of the disease in human and mosquito populations, respectively. Vaccination played a vital role in protecting humans from being infected thus reducing the spread of the disease. SIT significantly reduced the population of mosquitoes and the spread of malaria. Hence, we conclude that effective control of the spread of malaria requires measures that help control the disease in both human and mosquito populations as shown in this work. Plots were presented to show the dynamics of the disease.