Un modelo no-lineal de infección del VIH con terapia antirretroviral combinada

Abstract

In this work we study a nonlinear mathematical model of HIV infection with combined antiretroviral therapy proposed by Perelson and Nelson in 1999. These equations model the interaction between T-CD4 cells and viral particles of HIV infection. We considered the mechanism of virus replication when infecting T-CD4 lymphocytes, in addition to certain enzyme inhibitors used as pharmacological treatment. We perform a qualitative study of the model, finding its equilibrium points and using the Hartman-Grobman Theorem we obtain its local stability. By means of numerical simulations we visualized the behavior obtained. We obtained as a result that the behavior of the equilibrium states is summarized in a bifurcation transcribed under a threshold condition, being supported by the numerical simulations presented here.