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.
