Mathematical Modelling and Analysis of Autonomous HIV/AIDS Dynamics with Vertical Transmission and Nonlinear Treatment

In this study, a new mathematical model for human immunodeficiency virus (HIV) and acquired immune deficiency syndrome (AIDS) featuring vertical transmission and nonlinear treatment is presented. The model is analyzed through the implementation of some dynamical system tools with a view to assessing the behavior of trajectories of the system governing the dynamics of HIV/AIDS. The well-possedness of the formulated model is established via the theory of positivity and boundedness of solutions. Analysis of the model shows that the HIV/AIDS model exhibits backward bifurcation phenomenon in the presence of treatment delay. However, further investigation shows that the occurrence of backward bifurcation can be ruled out in the absence of treatment delay. Consequently, the global dynamics of the model around the disease-free and endemic equilibrium points in the absence of treatment delay is explored. It is shown that the model has a globally asymptotically stable disease-free equilibrium (endemic equilibrium) whenever the basic reproduction number is less than (greater than) unity accordingly. In addition, numerical simulations are performed to corroborate the theoretical results of the analysis, and the effects of various parameters of the model are graphically displayed.