where t 0 is the recovery time scale, i N the probability that a randomly selected individual is infected and d the probability that this individual recovers. Adopting t 0 as a reference, we assume that the higher the average number of contacts SkT, the smaller the time scale t INF at which infection update events occur (t INF~t0 =SkT) [3] . Hence, the rate of increasing the number of infected is given by