Approximate solution for a malaria model using the homotopy analysis method

Malaria as an infectious disease is 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 present a new model for the disease. The model incorporated vaccination, treatment and vector control using sterile-insect technology. Sensitivity analysis was performed to identify the parameters which affect the endemicity of the disease. The approximate solutions of the system were obtained using the homotopy analysis method. The results obtained showed the region of convergence for the solutions. Plots were used to show this convergence region, highlighting the advantage of HAM over many other approximation methods. MATLAB and Maple were used in the simulation and mathematical analysis.