Dynamic network data have become ubiquitous in social network analysis, with new information becoming available that captures when friendships form, when corporate transactions happen and when countries interact with each other. Moreover, data are available about individual actors in the network, including information about the spread of viral (disease or otherwise) processes between individuals in the network. We argue that the dynamics of these processes should be coupled with those of the network evolution in order to improve downstream inference and develop experimental and observational studies --- we do so by studying a class of stochastic epidemic models that are represented by a continuous-time Markov chain such that disease transmission is constrained by the contact network structure, and network evolution is in turn influenced by individual disease statuses. When aiming at estimating causal effect we couple this dynamic modeling with a study of the violation of classical no-interference assumptions, meaning that the treatment of one individuals might affect the outcomes of another. To make interference tractable, we consider a known network that describes how interference may travel. We discuss two settings: (1) design of experiments under known network interference and (2) an observational setting where the radius (and intensity) of the interference experienced by a unit is unknown and can depend on different sub-networks of those treated and untreated that are connected to this unit. In the former we propose an efficient design that leads to the naive difference in means estimator being consistent while in the second we show that under mild regularity conditions, an inverse weighted estimator is consistent, asymptotically normal and unbiased for the average treatment effect on the treated.