Recently I had the pleasure to hang out with Matt Silk from the University of Exeter: https://biosciences.exeter.ac.uk/staff/index.php?web_id=Matthew_Silk
It was great chatting about badgers, puma and network models over a few beers. His work summarizing statistical network models in Methods in Ecology and Evolution is particularly useful (see below).
After reading this you’ll know what ERGMS, TERGMs, REMs & SAOMs are and how they can answer network/disease questions. The only potentially useful addition I can see is generalized dissimilarity models (GDMs) as a robust way to test for covariate effects on network structure (as I did in my JAE 2017 paper). Anyway, this paper is certainly a good starting point for entering the world of statistical network analysis.