The first factor stands for the typical time scale at which infection events occur. The second factor represents the probability of randomly picking a healthy individual. This individual interacts with a random neighbor, who is infected with probability given by the third factor (well-mixed assumption). This contact leads to an additional infection with probability l. When r~0, Equations (M1) and (M2) describe both SIS and SI (d~0) models. We obtain the finite population analogue of the well-known meanfield equations characteristic of these models by recognizing that, in the limit of large populations, t 0 G i,r 