Table 1.

Values and confidence intervals for model parameters.

Parameter	Description	Best-fit value	95% CI	Source
${\beta }_{\mathrm{I}}$	Transmission rate for compartment $\mathrm{I}$	0.214	[0.184, 0.237]	Fitting
$\mathrm{a}={\beta }_{\mathrm{D}}/{\beta }_{\mathrm{I}}$	Ratio of transmission rates for$\mathrm{D}$ and $\mathrm{I}$	0.75	[0.5, 1]	(Fox et al, 2009, Marks et al, 2005)
$\mathrm{b}={\beta }_{\mathrm{T}}/{\beta }_{\mathrm{I}}$	Ratio of transmission rates for T and $\mathrm{I}$	0.1	[0.05, 0.15]	(Bunnell et al, 2006, Castilla et al, 2005, Donnell, 2010, Donnell et al, 2010, Granich et al, 2010, Quinn et al, 2000)
${\mathrm{d}}_{\mathrm{S}}$	Death rate for compartment $\mathrm{S}$	0.007	[0.00503, 0.0089]	Fitting
${\mathrm{d}}_{\mathrm{I}}$	Death rate for compartment $\mathrm{I}$	0.063	[0.045, 0.083]	(Collaborative group on AIDS incubation and HIV survival, including the CASCADE EU concerted action, 2000, Todd et al, 2007)
${\mathrm{d}}_{\mathrm{D}}$	Death rate for compartment $\mathrm{D}$	0.0427	[0.032, 0.055]	Data
${\mathrm{d}}_{\mathrm{T}}$	Death rate for compartment $\mathrm{T}$	0.0652	[0.051, 0.077]	Data
$\rho$	Treatment drop-out rate	0.0169	[0.0108, 0.025]	Data
${\mathrm{I}}_0$	Undiagnosed HIV positive population in 2005	813	[651, 934]	Fitting
$\Lambda$	Influx of susceptibles by birth and emigration	276	[199, 354]	Fitting
$\alpha \left(\mathrm{t}\right)$	Time-dependent diagnosis rate	$0.04345,\mathrm{t}\le 2004$ $0.0602\mathrm{t}-120.585,2004<\mathrm{t}\le 2007$ $0.55,2007<\mathrm{t}\le 2008$ $0.0602\mathrm{t}-120.585,2008<\mathrm{t}\le 2009$ $1,2009<\mathrm{t}\le 2010$ $0.0602\mathrm{t}-120.585,\mathrm{t}>2010$		Fitting
$\gamma \left(\mathrm{t}\right)$	Time-dependent treatment enrollment rate	$0,\mathrm{t}\le 2004$ $0.006228,2004<\mathrm{t}\le 2005$ $0\text{.}\text{01886t}-37\text{.}807,\mathrm{t}>2005$		Data
R2	Goodness of Fitting	0.97