Table 1 Definitions of the parameters used in the model
From: Personalized life expectancy and treatment benefit index of antiretroviral therapy
Variables | Definitions | Initial | Reference |
|---|---|---|---|
T | Uninfected CD 4+ cell population size | 1200 μ l −1 | |
T ∗ | Infected CD 4+ helper cell population size | 0 | |
V I | HIV population size | 100 μ l −1 | |
τ | Prolonged LE | interim variable | |
Parameters | baseline values [ranges] | ||
s | Rate of supply of CD 4+ T cell from precursors | 15 μ l −1 day −1 | [21] |
d | Death rate of uninfected CD 4+ T cells | 0.02 day −1 | [21] |
\(k(\bar {k})\) | Infection rate per virion | 2.1818×10−7 μ l −1 day −1(lk) | [21] |
δ | Death rate of infected CD 4+ T cells | 0.35 day −1[0.2 0.6] | [21] |
\(\lambda (\bar {\lambda })\) | Number of free virus produced by lysing a CD 4+ T cell | 3928.6 μ l −1 day −1(l λ) | [21] |
c | Death or clearance rate of free virus | 2.4 day −1 [1.5 3.5] | [21] |
\(\beta _{k}(\bar {\beta }_{k})\) | Scale parameter of Weibull function | 1500(225) [50-2000] | see text |
\(\beta _{\lambda }(\bar {\beta }_{\lambda })\) | Scale parameter of Weibull function | 200(200) [10-500] | see text |
\(\alpha _{k}(\bar {\alpha }_{k})\) | Shape parameter of Weibull function | 1.1(1.1) [0.2-2] | see text |
\(\alpha _{\lambda }(\bar {\alpha }_{\lambda })\) | Shape parameter of Weibull function | 0.04(0.04) [0.005-0.2] | see text |
T m | LE since infection without therapy | 11 [5,16] ×365 days | [34] |
\(\eta (\bar {\eta })\) | Drug efficacy of combination therapy | 0.95 [0.5 1] (q η) | [21] |
\(\tau _{50}(\bar {\tau }_{50})\) | Drug sensitivity of combination therapy | 30 [20, 100] ×365 days (p τ 50) | see text |
τ m | Maximum LE after infection | (T d −T s )days | – |
T d | Time of natural death | 74 ×365 days | [37] |
T s | Time to initiate treatment after infection | Determined by B CD4 | – |
T r | Time of emergence of drug resistant virus | Random variable in [T s ,T e ] | – |
T e | LE after infection with treatment | In [T m ,T d ] | – |
T 1000 | Time to virological failure | Determined by viral loads | – |
B CD4 | Baseline CD4 counts to initiate the treatment | 350 [100-450]cells/ μ l | – |
d a | Drug adherence rate | 90% [50-100%] | – |