Stochastic modeling of the dynamics of CD4+ T-cell infection by HIV and some Monte Carlo studies

In this paper, we develop a stochastic model for the interaction between CD4+ T cells and the human immunodeficiency virus (HIV) virus by taking into account the basic biological mechanism as described in [1–4]. We studied this stochastic model through extensive Monte Carlo simulations. Our results show that, in some cases, there is a positive probability that the virus will be eliminated by the process. We have also shown that, at the earlier stage of the infection, the probability distributions of the CD4+ T cells and free HIV are skewed; however, these distributions will eventually converge to the Gaussian distributions after several years. A real-data example is given to illustrate the application of our model.