MSM networks

STIsim provides three networks for modeling sexual contact between men. AgeMatchedMSM and AgeApproxMSM extend MFNetwork, inheriting risk groups, concurrency, and partnership classification, and differ only in how partners are matched. MSMScaleFreeNetwork extends BaseNetwork directly and uses a preferential-attachment kernel instead of risk groups.

Class	Matching strategy	When to use
sti.AgeMatchedMSM	Sort eligible males by age and pair sequentially	Lightweight; partners always have similar ages
sti.AgeApproxMSM	Reuses MFNetwork age-difference preferences to match split groups of eligible males	More flexible age mixing
sti.MSMScaleFreeNetwork	Preferential-attachment (rich-get-richer) degree kernel with Markovian edge deletion	Scale-free degree distribution; concentrated transmission

Participation

All three networks expose a p_msm parameter (default ss.bernoulli(p=0.015)) which sets the fraction of males that participate in MSM partnerships. Participation is assigned at sexual debut and is fixed for the lifetime of the agent.

msm = sti.AgeMatchedMSM(p_msm=ss.bernoulli(p=0.05))  # 5% of males

Combining with the heterosexual network

MSM networks are typically added alongside the default StructuredSexual network so that bisexual men contribute to transmission in both:

sim = sti.Sim(
    diseases='hiv',
    networks=[sti.StructuredSexual(), sti.AgeMatchedMSM()],
)

Each network maintains its own edges and partnership classification. Disease modules see contacts from all networks each timestep.

Scale-free network

sti.MSMScaleFreeNetwork (Whittles-2019 S2 kernel) forms edges via a rate proportional to a degree-based pair weight, producing a scale-free degree distribution where a minority of high-degree agents drive most transmission. Edges are deleted at random subject to a hard duration cap.

Parameter	Default	Description
p_msm	ss.bernoulli(p=0.015)	Fraction of males in the MSM pool
target_mean_degree	2.0	Target mean concurrent partners per pool agent
target_mean_dur	ss.years(2)	Target mean edge duration
max_edge_dur	ss.years(10)	Hard cap on edge persistence
phi	1.0	Turnover parameter (sets initial network density)

msm = sti.MSMScaleFreeNetwork(target_mean_degree=3.0)

Note: unlike the other networks, this one is not branching-stable under Common Random Numbers — adding an intervention that perturbs the population reshuffles edges from that point on. Reproducibility holds per (rand_seed, ti). It also does not record edge expirations, so analyzers that depend on them (e.g. PartnershipFormationAnalyzer) skip it.

API

• sti.AgeMatchedMSM — exact-age matching; cheap and deterministic given inputs.
• sti.AgeApproxMSM — distribution-based matching; reuses age-preference machinery from MFNetwork.
• sti.MSMScaleFreeNetwork — preferential-attachment kernel; scale-free degree distribution.