MATHEMATICALLY MODELING THE SPREAD OF HIV/AIDS INFECTION AFTER THE INTRODUCTION OF ANTIRETROVIRAL THERAPY IN GHANA.

Abstract

One of the deadliest and highly infectious diseases is Human Immunodeficiency Virus-Acquired Immune Deficiency Syndrome (HIV-AIDS). One person was first diagnosed with HIV-AIDS in the Eastern region part of Ghana in 1986, followed by 41 more in the same year. The spread of the disease was so unbearable in the subsequent years (1987-2003), even after several intervention measures taken by Government and other stakeholders. Hence, in 2003, the antiretroviral therapy (ART) program was introduced by the Ghana AIDS Commission (GAC) through the Ghana Health Service (GHS) to sabotage the virus such that it cannot be transmitted from one person to another, not even from the pregnant mother to the unborn child. It is in this direction that this research was conducted to use differential equations to derive a model for the prediction of the HIV/AIDS infection rate, after the introduction of the ART program in Ghana. The data on the number of HIV infected people per each year (I) for the years 2003-2018 were collated from the reports given by Ghana AIDS Commission (GAC), WHO and UNAIDS published on their associate websites. Differential equations, with the employment of numerical analysis of data, were used to derive a model for the prediction of the yearly number of HIV/AIDS infected people. Graphical analysis on the residuals of the predicted number of HIV/AIDS infected people (residual analysis) were carried out to check whether the derived model was adequate or not. Finally, a model was derived using ordinary differential equations and the yearly numbers of HIV infected people estimated using the model were in descending, order as portrayed in the original data set. The residual analysis on the model adequacy checking proved that the model is adequate for the prediction of the number of HIV infected people in Ghana. In effect, the ART program really played a major role in the reduction of the HIV infection rate. The uniqueness of this research is portrayed in the fact that it is the first time differential equation is being employed in Ghanaian academia to derive a model for the future prediction of the HIV infection rate.  

Keywords: Human Immunodeficiency Virus, Acquired Immune Deficiency Syndrome, antiretroviral therapy, HIV-Infected People, Susceptible People.