Table 1. Dynamic population model parameters and vaccine efficacy assumptions.

Notation±	Description	Units	Value or distribution	Justification
ϑ(a)	Rate of entering MSM population (by age)	Number/year	Skew-lognormal density function with location = 0.30, scale = 2.85, and skewness = 1.42	Fitted to self-reported age of first anal sex with a male partner by H2M study participants
μ(a)	Rate of exiting at-risk population (by age)¶	Per year	Weibull hazard function with shape = 3, location = 30, and scale = 25	Calibrated to obtain MSM population distribution akin to H2M study population*
$\overline{c}(a)$	Average rate of partner acquisition (by age)	Number/year	Parabolic function with maximum = 9.3 at 40 years	Fitted to estimated number of new anal sex partners in last 6 months (H2M study; Schorer Monitor†)
${\mathbb{p}}_k$	Fraction with sexual activity indexed by k	Percent	Variable according to model: {80%; 20%}, {90%; 10%}, or {60%; 30%; 10%}	Constrained by age-specific mean and coefficient of variation (cv = 1.86) of partner acquisition rate
${\mathbb{q}}_i$	Fraction with sexual preference indexed by i	Percent	Preference for either insertive, receptive, or both insertive and receptive anal sex: {13%; 13%; 74%}	Mixture model fitted to self-reported activities with anal sex partners by H2M study participants††
p	Conditional probability of having both insertive and receptive anal sex with the same partner	—	0.60 (applicable to MSM with preference for both insertive and receptive anal sex)	Mixture model fitted to self-reported activities with anal sex partners by H2M study participants††
ϕ	Assortativity with regard to preference for insertive/receptive anal sex	—	Variable according to model: 0.15 or 0.67	Chosen values denote random (0.15) and moderately strong assortative (0.67) mixing
ϵ	Assortativity with regard to sexual activity	—	Variable according to model: 0, 0.33, or 0.67	Chosen values denote random (0), weakly assortative (0.33), and moderately strong assortative (0.67) mixing
σ(a,t)	Rate of vaccine uptake (by age, after start of vaccination campaign)	Per year	Gamma function (from age ≥ 15 years) with shape = 2, scale = 2, and maximum = 0.02 in base-case scenarios	Fitted to hepatitis B vaccine uptake rates among 15- to 70-year-old MSM up to 2010 in the Netherlands
π	Probability of deriving vaccine-induced protection against future infections	—	0.85 in base-case scenarios; 1.0 in sensitivity analyses if fully susceptible at immunization, otherwise 0.0	Based on 85% incidence rate reduction of ≥6-month infection in male HPV vaccine trials (per-protocol)§
ϖ	Infection rate reduction induced by successful vaccination	—	1.0 in base-case scenarios; 0.85 in sensitivity analyses	Based on 85% incidence rate reduction of ≥6-month infection in male HPV vaccine trials (per-protocol)§

^±See mathematical descriptions for further explanation (S1 Text) and use in HPV16 transmission models (S2 Text).

^¶The at-risk population consists of MSM forming new sexual partnerships; those in steady monogamous relationships are no longer at risk.

*Approximated to the empirical density from age 45 years onward; density at younger age is distorted due to under-recruitment in the H2M study of MSM with recent sexual debut (see S3 Fig).

^†The Schorer Monitor is a large-scale internet survey investigating health, well-being, and sexuality among MSM throughout the Netherlands (see S1 Text).

^††The mixture model assumes identical proportions for MSM having strict preference for either insertive or receptive anal sex (see S1 Text).

^§As reported for vaccine-type infections detectable for at least 6 months in quadrivalent HPV vaccine trials among 16- to 26-year-old HIV-negative MSM (see [15,16]).

HPV, human papillomavirus; HPV16, human papillomavirus genotype 16; MSM, men who have sex with men.