Table 1.

Estimates of partnership and epidemic parameters

Parameter	Value	Definition	Source
1. Partnership parameters
$1/\left(\sigma +2\mu \right)$	271.5 days	Mean duration steady partnership	MSM data
$1/\rho P_0$	152.8 days	Mean time being single	MSM data
$1/\lambda$	12.3 days	Mean time between AI within steady partnership	MSM data
$P_0$	0.360	Fraction without a steady partner	MSM data
$P_1$	0.640	Fraction with a steady partner	MSM data
${\pi }_h$	0.337	Fraction high actives	MSM data
${\pi }_l$	0.663	Fraction low actives	MSM data
2. Parameters for condom use, PrEP and time to treatment			Source
$q_s$	54.1%	Mean condom use steady partner	MSM data
$q_c$	62.9%	Mean condom use casual partner	MSM data
$\xi$		Rate for a high active to start taking PrEP (calibrated to achieve different % PrEP coverage)	Varied
		Mean time from infection to successful antiretroviral treatment for a:
$1/{\gamma }_P$	0.25 years	High active on PrEP	27
$1/{\gamma }_h$	1.5–3 years	High active not on PrEP	Varied
$1/{\gamma }_l$	3.5–7 years	Low active	$1/{\gamma }_l=2.35/{\gamma }_h$
3. Casual sex partner parameters from data not using proxy			Source
		Mean time until new casual sex partner for a:
$1/{\alpha }_{0\bullet }^{h\bullet }$	10.7 days	High active when single	MSM data
$1/{\alpha }_{1\bullet }^{h\bullet }$	12.5 days	High active when in partnership	MSM data
$1/{\alpha }_{0\bullet }^{l\bullet }$	66.5 days	Low active when single	MSM data
$1/{\alpha }_{1\bullet }^{h\bullet }$	97.9 days	Low active when in partnership	MSM data
4. Casual sex partner parameters from data using proxy			Source
		Mean time until new casual partner for a high active with a:
$1/{\alpha }_{0\bullet }^{hh}$	14.1 days	High active when single	MSM data
$1/{\alpha }_{0\bullet }^{hl}$	43.7 days	Low active when single	MSM data
$1/{\alpha }_{1\bullet }^{hh}$	15.4 days	High active when in partnership	MSM data
$1/{\alpha }_{1\bullet }^{hl}$	66.4 days	Low active when in partnership	MSM data
		Mean time until new casual partner for a low active with a:
$1/{\alpha }_{0\bullet }^{lh}$	109.3 days	High active when single	MSM data
${\displaystyle 1/{\alpha }_0.}$	169.6 days	Low active when single	MSM data
$1/{\alpha }_{1\bullet }^{lh}$	136.1 days	High active when in partnership	MSM data
${\displaystyle 1/{\alpha }_1.}$	348.9 days	Low active when in partnership	MSM data
5. Parameters from the literature
	70%	Condom efficiency	28
$1/{\delta }_a$	0.24 years	Mean time in acute infection stage	18
$1/\mu$	60 years	Sexually active lifespan	29 30
		Per-act transmission probability
	0.1835	Acute stage URAI	16
	0.0138	Chronic stage URAI	16
	1.48%	Overall URAI	31
	0.62%	Overall UIAI	31
	2.39	Of URAI in comparison to UIAI	31
$p_A$	0.1301	Acute stage combined URAI-UIAI	16 31
$p_C$	0.0098	Chronic stage combined URAI-UIAI	16 31

AI, anal intercourse; MSM, men who have sex with men; PrEP, pre-exposure prophylaxis; UIAI, unprotected insertive anal intercourse; URAI, unprotected receptive anal intercourse.