Modelling a disease-relevant contact network of people who inject drugs

• We fit a social circuit ERGM for a contact network of injecting drug users.
• We describe use of conditional estimation for fitting ERGMs to snowball sampled data.
• We describe a novel, model-dependent estimator of population size.
• We simulate empirically grounded contact networks of injecting drugs users.
• We show that snowball data and snowball samples of simulated networks are similar.

This study uses social network analysis to model a contact network of people who inject drugs (PWID) relevant for investigating the spread of an infectious disease (hepatitis C). Using snowball sample data, parameters for an exponential random graph model (ERGM) including social circuit dependence and four attributes (location, age, injecting frequency, gender) are estimated using a conditional estimation approach that respects the structure of snowball sample designs. Those network parameter estimates are then used to create a novel, model-dependent estimate of network size. Simulated PWID contact networks are created and compared with Bernoulli graphs. Location, age and injecting frequency are shown to be statistically significant attribute parameters in the ERGM. Simulated ERGM networks are shown to fit the collected data very well across a number of metrics. In comparison with Bernoulli graphs, simulated networks are shown to have longer paths and more clustering. Results from this study make possible simulation of realistic networks for investigating treatment and intervention strategies for reducing hepatitis C prevalence.