Mathematical Modelling of Dynamics of HIV Transmission Depicting the Importance of Counseling and Treatment

Abstract

Human immunodeficiency virus is an incurable disease which attacks and destroys the human immune
system thereby making the body susceptible to all kinds of illnesses. If left unattended to, it can lead to the damaging of
body organs such as the brain, kidney and the heart which can result to death. Unfortunately this disease has no known
cure till date but through counseling and administering of antiretroviral drugs, the likelihood of dying from it becomes
minimal. This study presents the deterministic HIV transmission model. The model has a unique endemic equilibrium point which is locally asymptotically stable if R₀  > 1 , DFE of the model was obtained and is shown to be Local
asymptotically stable when the associated basic reproduction number was R > 1. We established the numerical simulation of the model which shows that the effective use of condom, counseling or the use of anti-retrovirus drug can lead to effective reduction on HIV transmission. Finally, we discussed that the ART treatment rate will reduce the basic reproduction number R₀ hence, leading to the extinction of HIV/AIDS.