Table 1.

Model parameters.^a

Parameter		Value	Source
Progression rate active CHB to inactive, per year	${\theta }_{23}$	0.1	[21], [22]
Progression rate inactive to active CHB, per year	${\theta }_{32}$	0.02	[21], [22], [23]
Progression rate active CHB to compensated cirrhosis, per year	${\theta }_{24}$	0.05	[21]
Progression rate compensated to decompensated cirrhosis, per year	${\theta }_{45}$	0.02	[24], [25]
Progression from active CHB to HCC, per year	${\phi }_2$	0.003	[21]
Progression from inactive to HCC, per year	${\phi }_3$	0.0002	[21]
Progression from compensated cirrhosis to HCC, per year	${\phi }_4$	0.02	[21], [26]
Progression from decompensated cirrhosis to HCC, per year	${\phi }_5$	0.04	[26]
Death rate from compensated cirrhosis, per year	${\mu }_4$	0.033	[24], [27]
Death rate from decompensated cirrhosis, per year	${\mu }_5$	0.25	[24], [28]
Death rate from HCC, per year	${\mu }_6$	0.35	[29], [30]
Probability acute infection progresses to chronic	$\sigma$	0.07	[31]
Transition rate out of acute infection, per year	${\theta }_1$	4	[32]
HBV clearance rate from chronic infection, per year	${\theta }_{2z},{\theta }_{3z}$	0.01	[33], [34]
HBV clearance rate from compensated cirrhosis, per year	${\theta }_{4z}$	0.02	[33], [34]
% new HBV infections notified during acute phase	$f_s$	10–30%	[35], [36]
Progression rate treated (T) to HCC (W8), per year	${\phi }_T$	0.0002	[37], [38], [39], [40]
HBV-related death rate for those treated, per year	${\mu }_T$	0.001	[37], [38], [39], [40]
Treatment rate active CHB, compensated cirrhosis, per year	$\tau$	$\tau ={\tau }_c\ast {\tau }_s$
% of diagnosed under treatment, until 2011	${\tau }_c$	50–70%	Assumption
% of diagnosed under treatment, from 2012 onwards	${\tau }_c$	70–90%	[41]
% Virally suppressed among treated, until 2011	${\tau }_s$	60–80%	[37], [42], [43]
% Virally suppressed among treated, from 2012 onwards	${\tau }_s$	91–99%	[37], [42], [43]
Rate of entry into and exit out of population, per year	$\mu$	0.02	*
Number of MSM	$N$	144,521–263,309	[44]
Probability HBV transmission per act CAI if infected in state $i=1,2,\cdots ,6,T$	${\beta }_i$	${\beta }_i=f_i\ast \beta$
Probability HBV transmission per act CAI if infected has inactive chronic HBV	$\beta$	0.001–0.01	Assumption
Relative transmissibility acute HBV, compared to inactive chronic HBV	$f_1$	15–35	[45]
Relative transmissibility active CHB, compared to inactive chronic HBV	$f_2$	10–20	[46]
Relative transmissibility compensated cirrhosis, compared to inactive chronic HBV	$f_4$	10–20	[46]
Transmissibility decompensated cirrhosis, HCC	NA	NA	**
Relative transmissibility if virally suppressed, compared to inactive chronic HBV	$f_T$	0.05–0.15	[38], [39], [40], [43]
% Reduction probability to acquire HBV due to HBV-related antiretrovirals for HIV	${\psi }_c$	85–95%	[47], [48]
% Reduction in probability to acquire HBV infection among those receiving PrEP	${\psi }_p$	88–92%	[49]
Assortative mixing in steady or casual partnerships, respectively	${\epsilon }_S$, ${\epsilon }_C$	70%, 50%	Assumption
Factor increasing CAI frequency before 2002 compared to 2002 and thereafter		1–30%	Assumption

^aParameters with a range were included in the Latin Hypercube Sampling.

^*Assuming sexual activity for MSM 15–64 years old.

^**Assuming that individuals with decompensated cirrhosis or HCC do not engage in sexual practices that could lead to transmission, due to the severity of this phase. Abbreviations: HBV, hepatitis B virus; MSM, men who have sex with men; CHB, chronic hepatitis B; HCC, hepatocellular carcinoma; PrEP, pre-exposure prophylaxis; CAI, condomless anal intercourse.