HIV and Sexually Transmitted Infection Epidemic Potential of Networks of Men Who Have Sex With Men in Two Cities

Abstract

Background: The speed with which a pathogen circulates in a sexual network is a function of network connectivity. Cross-sectional connectivity is a function of network features like momentary degree and assortative mixing. Temporal connectivity is driven by partner acquisition rates. The forward-reachable path (FRP) has been proposed as a summary measure of these two aspects of transmission potential. We use empirical data from San Francisco and Atlanta to estimate the generative parameters of the FRP and compare results to the HIV/sexually transmitted infection epidemics in each city.

Methods: We used temporal exponential random graph models to estimate the generative parameters for each city's dynamic sexual network from survey data. We then simulated stochastic dynamic networks from the fitted models and calculated the FRP for each realization, overall, and stratified by partnership type and demographics.

Results: The overall mean and median paths were higher in San Francisco than in Atlanta. The overall paths for each city were greater than the sum of the paths in each individual partnership network. In the casual partnership network, the mean path was highest in the youngest age group and lowest in the oldest age group, despite the fact that the youngest group had the lowest mean momentary degree and past-year partner counts.

Conclusions: The FRP by age group revealed the additional utility of the measure beyond the temporal and cross-sectional network connectivity measures. Other nonnetwork factors are still necessary to infer total epidemic potential for any specific pathogen.

Figure 1.

The network analysis process. Step (1a): Estimate individual-level empirical network measures. Step (1b): Combine estimates from 1a with population-level demographic weights to estimate population-level empirical network statistics. Step (2): Fit network models using exponential random graph models (ERGMs) for one-time partnerships and temporal ERGMs for partnerships with duration (main and casual partnerships). Inputs for these models come from step 1b. Step (3): Simulate the complete networks over time for each city. Step (4): Estimate and compare the forward reachable paths (FRPs) for each city.

Figure 2.

Estimated distribution of forward reachable path (FRP) evolution over a 5-year period for casual and one-time sexual partnership networks of MSM in San Francisco and Atlanta. Each line represents the trajectory of connectivity in the network over time, for a specific node from time 0. Casual partnerships are defined as an ongoing relationship, but not a main partner, and one-time as partnerships are those without duration, occurring only once. The number connected, or reachable within the network, is on the Y-axis and the time step in weeks is the X-axis.

Figure 3.

Estimated distribution of forward reachable path (FRP) evolution over a 5-year period for main sexual partnership networks of MSM in San Francisco and Atlanta. Each line represents the trajectory of connectivity in the network over time, for a specific node from time 0. Main partnerships are defined as partners considered a boyfriend, significant other, or life partner. The number connected, or reachable within the network, is on the Y-axis and the time step in weeks is the X-axis.

Figure 4.

Average proportion of the San Francisco (solid lines) and Atlanta (dashed lines) populations connected within sexual networks of casual partnerships of MSM over a 5-year period by age category. The Y-axis shows the average proportion of the 10,000 MSM connected, or reachable, in the network over time. The X-axis shows the time step in weeks. In San Francisco, reachability ranged from around 40-65% over 5-years, whereas in Atlanta, reachability ranged from around 4–8% over 5-years.