Skip to main content

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%]
  1. where l,p,q are modification factors related to corresponding parameters with l=0.935,p=3,q=1 as baseline values. And \(\bar {k}=lk, \bar {\lambda }=l\lambda \), \(\bar {\tau }_{50}=p\tau _{50}\), \(\bar {\eta }=q\eta \). Note that over bar represents the same parameter but with values corresponding to with ART and/or drug resistance