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Zbl 0946.92011
Mittler, John E.; Sulzer, Bernhard; Neumann, Avidan U.; Perelson, Alan S.
Influence of delayed viral production on viral dynamics in HIV-1 infected patients. (English)
[J] Math. Biosci. 152, No.2, 143-163 (1998). ISSN 0025-5564

Summary: We present and analyze a model for the interaction of human immunodeficiency virus type 1 (HIV-1) with target cells that includes a time delay between initial infection and the formation of productively infected cells. Assuming that the variation among cells with respect to this `intracellular' delay can be approximated by a gamma distribution, a highly flexible distribution that can mimic a variety of biologically plausible delays, we provide analytical solutions for the expected decline in plasma virus concentration after the initiation of antiretroviral therapy with one or more protease inhibitors. We then use the model to investigate whether the parameters that characterize viral dynamics can be identified from biological data.\par Using nonlinear least-squares regression to fit the model to simulated data in which the delays conform to a gamma distribution, we show that good estimates for free viral clearance rates, infected cell death rates, and parameters characterizing the gamma distribution can be obtained. For simulated data sets in which the delays were generated using other biologically plausible distributions, reasonably good estimates for viral clearance rates, infected cell death rates, and mean delay times can be obtained using the gamma-delay model. For simulated data sets that include added simulated noise, viral clearance rate estimates are not as reliable. If the mean intracellular delay is known, however, we show that reasonable estimates for the vital clearance rate can be obtained by taking the harmonic mean of viral clearance rate estimates from a group of patients. These results demonstrate that it is possible to incorporate distributed intracellular delays into existing models for HIV dynamics and to use these refined models to estimate the half-lift of free virus from data on the decline in HIV-1 RNA following treatment.

MSC 2000:: *92C50 Medical appl. of mathematical biology
92D30 Epidemiology
45J05 Integro-ordinary differential equations
62J02 General nonlinear regression

Keywords: AIDS; viral load; antiretroviral therapy; protease inhibitors; ordinary differential equations; HIV-1; time delay; viral dynamics; nonlinear least-squares regression

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Zentralblatt MATH Berlin [Germany]