Stability properties of a delayed HIV infection model with absorption and apoptosis

Abstract

The mathematical theory of viral infections has enhanced our knowledge of the dynamics of viral infections and allowed us to determine the efficiency of antiviral therapy. In this study, we formulated the stability properties of a modified HIV virus infection model by considering the absorption effect, which is distinguished from the existing HIV virus models. The apoptosis effect is incorporated into the model with absorption effect, which is the novel concept. To strengthen the biological realism of the processes, intracellular time delay was incorporated into this model by using system of delay differential equations. This study was conducted to illustrate the stability of the model and how the time delay affects it. Stability properties of feasible equilibriums were established by analyzing characteristic equations in the presence and absence of time delay. Furthermore, non-negativity and the boundedness of solutions of the model were also established. It is demonstrated that the infection-free equilibrium is locally asymptotically stable if the basic reproduction number is less than unity. Besides, it is proven that chronic infection equilibrium is locally asymptotically stable if the basic reproduction number is greater than unity. Moreover, numerical simulations were carried out in order to perform the validity of theoretical results obtained utilizing MATLAB, which indicate that intracellular time delay has a significant impact on disease eradication and that the basic reproduction number is solely responsible for the model's dynamics because the basic reproduction number totally depends on the delay term of the delay differential equations.