A mathematical model for transmission dynamics of HIV/AIDS with effect of weak CD4+ T cells

Abstract

A mathematical model is proposed for the dynamics of HIV/AIDS with incorporation of weak CD4+ T cells. The model considers three different categories of cells: uninfected CD4+ T cells, infected CD4+ T cells, and virus. The anticipated model helps to illustrate the many of mystifying features of HIV infection more clearly. This model demonstrates two steady states: an infection-free equilibrium state, in which there is no virus, and an infection equilibrium state, in which virus and infected T cells are present. We have also calculated the local stability of the infection-free equilibrium and infection equilibrium for the model when the valuable reproduction number is less than and greater than one. With the help of Lyapunov's second method and the geometric approach, we are defining the novel conditions for the global stability of infection-free equilibrium state and infection equilibrium state. This study, which knocks off-balance the system, is articulated by a small variation of the parameters conceded by the system from one stable state to an unstable state. The dynamics of this new steady state are calculated both numerically and via the stability analysis.