All individual-based simulations start from a complete network of size N = 100. Disease spreading and network evolution proceed together under asynchronous updating. Disease update events take place with probability 1zt ð Þ {1 , where t~t NET =t DIS and t DIS~1 , network update events occur otherwise. For network update events, we randomly draw two nodes from the population. If connected, then the link disappears with probability given by the respective b pq . Otherwise, a new link appears with probability c. When a disease update event occurs, a recovery event takes place with probability 1zSkT ð Þ {1 , an infection event otherwise. In both cases, an individual j is drawn randomly from the population. If j is infected and a recovery event has been selected then j will become susceptible (or recovered, model dependent) with probability d. If j is susceptible and an infection event occurs, then j will get infected with probability l if a randomly chosen neighbor of j is infected. The quasi-stationary distributions shown in Figure 1 are computed as the fraction of time the population spends in each configuration (i.e., number of infected individuals) during 10 9 disease event updates (10 7 generations). The average number of infected SIT and the mean average degree of the network SkT Ã observed during these 10 7 generations are shown in Figure 3 . The results reported are independent of the initial number of infected in the network. Finally, the disease progression in time, shown in Figure 4b , is calculated from 10 4 independent simulations, each simulation starting with 1 infected individual. The reported results correspond to the average amount of time after which the population reaches a state with i infected.