University of Washington - Department of Statistics
Mathematical models are instrumental in understanding the progression of contact-based infectious diseases. These models implicitly rely on an underlying network of partnerships, and it is important for these partnership networks to reflect important structures in the population of interest. In particular, concurrent partnerships and assortative mixing can greatly affect the prevalence of a disease in a population and explain heterogeneity we observe. We show how mixing totals and concurrency, as given by momentary degree distributions, can simultaneously be estimated from egocentric data. We then describe how these can be used by exponential family random graph models (ERGMs) to simulate partnership networks consistent with the observed mixing totals and momentary degree distributions. As an alternative to ERGMs, we demonstrate the use of sequential importance sampling (SIS) in generating partnership networks that match desired momentary degree distributions exactly. Finally, we consider the application of revealed preference models (RPM) and two-sided matching models to generating partnership networks with these desired network structures. Our results suggest that ERGMs are still preferable to SIS and RPMs, although RPMs produce credible results for certain momentary degree distributions.