Stochastic modeling of the dynamics of $$CD4^ +$$ $$T$$-cell infection by HIV and some Monte Carlo studies.(English)Zbl 0887.92021

Summary: We develop a stochastic model for the interaction between $$\text{CD}4^+ \text{T}$$ cells and the human immunodeficiency virus (HIV) by taking into account the basic biological mechanism as described, e.g., by A. S. Perelson et al. [Math. Biosci. 114, No. 1, 81-125 (1993; Zbl 0796.92016)], D. Schenzle [Stat. Med. 13, 2067-2079 (1994)]. 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 $$\text{CD}4^+ \text{T}$$ 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.

MSC:

 92C50 Medical applications (general) 92C60 Medical epidemiology 65C05 Monte Carlo methods

Keywords:

human immunodeficiency virus; HIV

Zbl 0796.92016
Full Text:

References:

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