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%] | – |