A Mathematical Model for Effective Control and Possible Eradication of Malaria

Abstract

In this paper, a deterministic mathematical model for the transmission and control of malaria is formulated. The main innovation in the model is that, in addition to the natural death rate of the vector (mosquito), a proportion of the prevention efforts also contributes to a reduction of the mosquito population. The motivation for the model is that in a closed environment, an optimal combination of the percentage of susceptible people needed to implement the preventative strategies $\left(\alpha \right)$ and the percentage of infected people needed to seek treatment can reduce both the number of infected humans and infected mosquito populations and eventually eliminate the disease from the community. Prevention effort $\alpha$ was found to be the most sensitive parameter in the reduction of ${\mathrm{ℛ}}_0$ . Hence, numerical simulations were performed using different values of $\alpha$ to determine an optimal value of $\alpha$ that reduces the incidence rate fastest. It was discovered that an optimal combination that reduces the incidence rate fastest comes from about $40\%$ of adherence to the preventive strategies coupled with about $40\%$ of infected humans seeking clinical treatment, as this will reduce the infected human and vector populations considerably.