Let us start by introducing the well established SIS model [1, 3] , whereby individuals can be in one of two epidemiological states: Infected (I) or Susceptible (S). Individuals occupy the nodes of a graph, whereas the links of the graph define who interacts with whom. As usual, we define a transmission probability l and a recovery probability d. We assume a population of finite and constant size N, but with variable number of links [39, 40] . Links are established and removed at rates which also depend on the health status of the individuals connected: Links of different types -SS, SI and II -will tend to last differently. The SIR model, on the other hand, requires the introduction of a new epidemiological state -Recovered (or Removed, R) -representing individuals who, once recovered from the infection, acquire immunity. In SIR, the same parameters l and d defined above remain finite, but now we have three new kinds of links -SR, RI and RR. Finally, the SI model can be viewed as the limit of the SIS model when d~0, representing diseases from which recovery is impossible.