مشخصات پژوهش

In this paper, by the theory of dynamical systems, the local and global stability of an HIV viral infection model will be studied. These results will be given by using Lyapunov’s second method and LaSalle’s invariance principle. We will find the equilibria of the system and prove the local and global stability of these points by the value of the basic reproduction number. Some numerical examples will be presented to review the theoretical results. Finally, by including the effects of drug therapy on the model, we will introduce a new threshold parameter. Here, without any extra condition, we will prove that if the basic reproduction number is greater than one, then positive equilibrium is always globally asymptotically stabl. We will give some basic properties of the solutions, find the equilibria of the system and study the local stability of these points. Then, using Lyapunov’s second method and LaSalle’s invariance principle, some sufficient conditions will be given about the global stability of the equilibria. Numerical analysis will be then presented to illustrate our analytical findings. Moreover, drug efficacy will be discussed and finally the paper ends with a discussion of the obtained results in the previous sections.