Sirs-Si Model of Malaria Disease with Application of Vaccines, Anti-Malarial Drugs, and Spraying

Abstract

Malaria is a deadly disease transmitted to humans through the bite of infected female mosquitoes .It can also be transmitted from an infected mother (congenitally) or through blood transfusion. In this paper, we discussed the transmission of malaria featuring in the framework of an SIRS-SI model with treatments are given to humans and mosquitoes. We here utilized the use of vaccines, the use of anti-malarial drugs, and the use of spraying as treatment efforts. A stability analysis was then performed and numerical simulation was provided to clarify the result. It is shown that treatments affect the dynamics of human and mosquito populations. In addition, we proposed the Homotopy Analysis Method (HAM) to construct the approximate solution of the model.