Mathematical Modelling of the Causes, Dynamic Transmission and Control of Malaria Disease

Malaria is an infectious disease caused by the Plasmodium parasite and spreads between humans via female Anopheles mosquito bites. A mathematical model describes the dynamics of malaria and human population compartments in the form of mathematical equations, which represent the relationships between the compartments’ key attributes. The goal of this study id to identify the key parameters involved in the transmission and spread of the endemic malaria disease, as well as to try to discover acceptable solutions and techniques for the prevention and control using mathematical modelling. The malaria model is built on basic mathematical modelling approaches that result in a system of ordinary equations (ODEs). Our study examines the stability of the model’s equilibrium points. We found that if the reproduction number R 0 is smaller the 1 (R 0 1), the disease-free equilibrium becomes unstable. In that situation, the endemic state has a distinct equilibrium, re-invasion is always possible, and the disease remains in the human population. We used the Newton-Raphson method to iterate and successfully find better approximations to the values of the compartments of both the human and vector populations of the model at the endemic equilibrium. Also numerical simulations were carried out using the numerical software Python. These simulations demonstrate the behavior of populations over time as well as the stability of disease-free and endemic equilibrium points.