An HIV/AIDS Model with Vertical Transmission, Treatment and Progression Rate

Abstract

The Human Immunodeficiency Virus (HIV) infection which leads to Acquired Immunodeficiency Syndrome (AIDS) has become a deadly infectious disease in both developed and developing nations. It usually breaks down the body immune system, leaving the victim vulnerable to a lot of other diseases. Therefore, in this study a nonlinear mathematical model of HIV/AIDS with treatment, vertical transmission and progression rate were considered. The basic reproduction number (R0) was evaluate by next generation matrix and the global stability was examine by the comparison approach. The disease – free and the endemic equilibrium of the model were determined by setting all compartments to be zero. The sensitivity analysis was carried out to determine the parameter that has high impact on the spread of the disease using partial derivatives and the Maple software 14 was used for numerical simulation of the model. The disease free and endemic equilibrium were obtained and their stabilities studied. The model showed that the disease free equilibrium is locally asymptotically stable by using Routh-Hurwitz criteria and globally the disease free equilibrium is stable by comparism approach. The numerical simulation showed that by using treatment measures and controlling the rate of vertical transmission with time, the spread of the disease can be reduced significantly and by providing treatment at the pre-AIDs stage reduces the infection much faster than starting treatment after progression into AIDs.