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Assessing effects of HIV heterogeneity and macrophage on the HIV pathogenesis in HIV-infected individuals. (English) Zbl 0962.92023
Summary: Taking into account the real world situations, we have developed a stochastic model of HIV pathogenesis in HIV-infected individuals under very general conditions. In this model, we have considered five different types of $$\text{CD4}^{(+)}T$$ cells, two different types of HIV $$(M$$-tropic versus $$T$$-tropic) as well as infected and un-infected macrophage. This is a 9-dimensional stochastic process. For this process, we have developed stochastic differential equations for different types of cells. By using these stochastic equations, we have generated some Monte Carlo data to study the stochastic behavior of the HIV pathogenesis and the HIV progression.
Through Monte Carlo studies, we have revealed an acute infection stage in the early stage of the HIV infection and have confirmed the basic role played by lymph nodes and some long-lived cells such as macrophage in serving as reservoirs of HIV to escape elimination by the immune system during the long asymptomatic stage of HIV infection. The Monte Carlo results have shown that the HIV heterogeneity and diversity may be a major factor to determine the time period since infection for uninfected $$T$$ cells to drop to below $$\text{200/mm}^3$$ of blood. The numerical results have also confirmed our previous findings [see {it W.-Y. Tan} and H. Wu, Math. Biosci. 147, No. 2, 173-205 (1998; Zbl 0887.92021)] which concluded that the probability distributions of $$T$$ cells and free HIV can be classified into three periods over time: The latent period, the transition period and the pseudo-steady period.
##### MSC:
 92C50 Medical applications (general) 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60H35 Computational methods for stochastic equations (aspects of stochastic analysis) 60G35 Signal detection and filtering (aspects of stochastic processes)
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