MATHEMATICAL MODELLING OF CAUSES AND CONTROL OF MALARIA

Abstract

Malaria is a global health concern, with Africa bearing the highest global burden of malaria, as plasmodium falciparum malaria remains the leading cause of malaria-related mortality on the continent. This paper shows a mathematical model which describes the dynamics of malaria and human population compartments in terms of mathematical equations and these equations represent the relationship between relevant properties of the compartments. The malaria model is developed based on basic mathematical modelling techniques leading to a system of ordinary differential equations (ODEs) with 4 variables for humans and 3 variables for mosquitoes. Qualitative analysis of the model applies dimensional analysis, scaling, and perturbation techniques in addition to stability theory for ODE systems. We also derive the equilibrium points of the model and investigate their stability. In that case, the endemic state has a unique equilibrium, re-invasion is always possible, and the disease persists within the human population.