Abstract

TORO-ZAPATA, Hernán Darío; ROA-VASQUEZ, Enmanuel  and  MESA-MAZO, Mónica Jhoana. Stochastic model for the HIV infection of T CD4 ⁺ cells in immune system. Rev. Mat [online]. 2017, vol.24, n.2, pp.287-313. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v24i2.29870.

In this paper we study the dynamics of HIV infection through the stochastic birth and death processes and ordinary differential equations representing a real system. For this specific case, a stochastic process is described to interpret the dynamics of HIV infection within a person’s organism in the initial stages of infection (post exposure or window period); that is to say, the initial time for the model corresponds with the very moment the virus enters the organism, and from then on the process of replication is taken into account and the incidences that the virus generates when it attacks the CD4+ T cells, which are integral parts of the patient’s immune system. The stochastic process allows one to deduce from first principles and create a basic model for HIV infection. The model is similar to those studied in the literature. It is a system based on ordinary differential equations with stochastic states. The state variables correspond to expected values (averages). We also find differential equations for the variance of the stochastic state of the variables, which provides additional information about the system. Finally, we present the local analytical study of the complete model and a numerical study of the system solutions using values of the parameters. The values of the parameters were obtained from secondary sources and were used to illustrate the analytical results.

Keywords : stochastic processes; dynamical system; local stability; HIV; AIDS.

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