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Modeling the interaction of the immune system with HIV. (English) Zbl 0683.92001
Mathematical and statistical approaches to AIDS epidemiology, Lect. Notes Biomath. 83, 350-370 (1989).

Summary: [For the entire collection see Zbl 0682.00023.]

The interactions between the human immune system and HIV are potentially complex. In this paper I review some of these interactions and sketch the beginnings of a general model that can potentially account for many of the immunological consequences of HIV infection. This model involves a large number of ordinary differential equations and many parameters. To make progress, I simplify the general model and develop a four-equations model that involves free HIV and uninfected, latently infected and actively infected CD4 + T cells. Using reasonable guesses for parameter values, I show that this model can account for some of the puzzling features of AIDS: the long latent period, the almost complete absence of free virus particles, the low frequency of infected T4 cells and the slow T cell depletion seen during the course of the disease. Further, the model suggests why the latent period may be significantly shorter in children than in adults.

MSC:
92C50Medical applications of mathematical biology
92D25Population dynamics (general)