In this section, we use the word "analytic" broadly, to imply models that are directly numerically integrable, without the use of Monte Carlo simulation methods, rather than systems for which all results can be written in terms of fundamental functions, of which there are very few in epidemiology. Analytic approaches to transmission of infection on networks fall into three broad categories. Firstly, there are approaches that calculate exact invasion thresholds and final sizes for special networks. Secondly, there are approaches for calculating exact transient dynamics, including epidemic peak heights and times, but again, these only hold in special networks. Finally, there are approaches based on moment closure that are give approximately correct dynamics for a wide class of networks.