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Abstract
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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.
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