Virus models are used commonly for modeling and analysis of biological networks, computer networks, and human contact networks. The dynamic modeling of such systems in prior work has mainly been focused on networks with static graph structures, which we posit are unrealistic and/or oversimplified for the purpose of understanding and analyzing disease propagation of viruses. In this paper, we consider network models with dynamic graph structures, and investigate the propagation and inhibition of diseases in these systems. A stability analysis of the model we consider is performed, examining the disease free equilibrium conditions. Quarantine is proposed as one control technique. Various network simulations are presented and a number of conjectures are given based on these simulations.