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A model of HIV-1 pathogenesis that includes an intracellular delay. (English) Zbl 0942.92017

Summary: Mathematical modeling combined with experimental measurements have yielded important insights into HIV-1 pathogenesis. For example, data from experiments in which HIV-infected patients are given potent antiretroviral drugs that perturb the infection process have been used to estimate kinetic parameters underlying HIV infection. Many of the models used to analyze data have assumed drug treatments to be completely efficacious and that upon infection a cell instantly begins producing virus. We consider a model that allows for less then perfect drug effects and which includes a delay in the initiation of virus production.

We present detailed analysis of this delay differential equation model and compare the results to a model without delay. Our analysis shows that when drug efficacy is less than $100%$, as may be the case in vivo, the predicted rate of decline in plasma virus concentration depends on three factors: the death rate of virus producing cells, the efficacy of therapy, and the length of the delay. Thus, previous estimates of infected cell loss rates can be improved upon by considering more realistic models of viral infection.

MSC:
 92C50 Medical applications of mathematical biology 34K60 Qualitative investigation and simulation of models 92C60 Medical epidemiology