described in: **A model of HIV-1 pathogenesis that includes an intracellular delay.**

Nelson PW, Murray JD, Perelson AS; *Math Biosci.*
2000 Feb;163(2):201-15. PMID: 10701304
; doi: 10.1016/S0025-5564(99)00055-3

**Abstract:**

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.

**Author Keywords:**
HIV; Delay; Viral life cycle; T-cells

As the initial conditions for the intergrations where not known, approximate inital conditions for the steady state at *k=3.47*10 ^{-8}
*
where chosen (

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uninfected T-cells

infected T-cells

infectious virius (V _{I}
)

non-infectious virus (V _{NI}
)

delay between T-cell infection and lysis

virions released per cell upon lysis

proetease inhibitor efficacy