Mathematical Modelling Of Causes And Control Of Malaria

Malaria, an infectious disease caused by the Plasmodium parasite, is transmitted between humans through the bites of female Anopheles mosquitoes. To understand and manage this disease, mathematical modeling describes the dynamics of malaria transmission and the interactions between human and mosquito populations using mathematical equations. These equations detail the relationships between different variables within the compartments of the model. The study aims to identify key parameters influencing the transmission and spread of endemic malaria and to develop effective prevention and control strategies through mathematical analysis. The malaria model employs fundamental mathematical techniques, resulting in a system of ordinary differential equations (ODEs) with four variables for humans and three for mosquitoes. Qualitative analysis of the model includes dimensional analysis, scaling, perturbation techniques, and stability theory for ODE systems. The model’s equilibrium points are derived and analyzed for stability, revealing that the endemic state has a unique equilibrium where the disease persists, and re-invasion remains possible. Simulations demonstrate the temporal behavior of the populations and the stability of both disease-free and endemic equilibrium states. Numerical simulations suggest that combining insecticide-treated bed nets, indoor residual spraying, and chemotherapy is the most effective approach for controlling or eradicating malaria. However, reducing the biting rate of female Anopheles mosquitoes through the use of insecticide-treated bed nets and indoor residual spraying proves to be the most crucial strategy, especially as some antimalarial drugs face resistance.