|
Abstract
|
Biomathematics is one of the most important interdisciplinary research area which has recently
attracted the attention of many researchers and scientists. In this area, population dynamics, biochemical
reactions and infectious diseases are modeled with mathematical tools such as differential equations. After
modeling, applying nonlinear analysis methods, the dynamical behavior of the model is checked. 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 using Lyapunov’s second method and LaSalle’s invariance
principle. We will find the equilibrium points of the system and prove the local and global stability of these
points based on the values of the basic reproduction number (R0). It will be proven that if R0 ≤ 1, then the
virus-free equilibrium E0 is globally stable and the viruses are cleared. If R0 > 1, then there exists a chronic
equilibrium E∗ which is globally stable and the infection becomes chronic. 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.
|