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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.

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