An Epidemiological Model of Malaria Transmission in Ghana

Abstract

In this paper malaria was modelled as a 7-dimensional system of ordinary differential equations. Analysis of the model showed that there exists a domain where the model is epidemiologically and mathematically well-posed. The basic reproduction number,() was computed. The stability analysis of the model was investigated and proved that the disease-free equilibrium is locally asymptotically stable if () and unstable when (). The Centre Manifold theorem is used to show that the model has a unique endemic equilibrium which is locally asymptotically stable when (). Sensitivity analysis was applied to find which parameters impacts the basic reproduction number the most, it was observed that the most sensitive parameters are mosquitoes biting rate () and mosquitoes death rate (). Simulations using MATLAB and the fourth order Range-Kutta numerical method was done to determine the effectiveness of all possible combinations of malaria control measures and the numerical results shows that the combination of four (4) control measures have the highest impact on the control of the disease. Also with individuals total adherence to effective use of treated bednets and spray of insecticide for at least 70 days in the population, little treatment efforts will then be required by the Ghanaian population in the control of the spread of Malaria.