The network dynamics proposed here differs from those used in previous models of disease spreading on adaptive networks [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] . Similar to most models, the population size remains fixed. Unlike most of these studies, however, we do not impose any local or global linking constraints, meaning that individuals can create (or remove) a link without the need for removing (or creating) another one -in other words, the number of links will change in time, also adapting to the disease configuration of the population. Consequently, the average degree of the network results from the self-organization of the network structure, and co-evolves with the disease dynamics (cf. networks evolving towards critical values of connectivity, as studied in [45] ). A population suffering from high disease prevalence where individuals avoid contact in order to escape infection will therefore exhibit a lower average degree than a population with hardly any infected individuals. Such a frequency-dependent average degree prevents also that containment of infected individuals would result automatically in the formation of a dense healthy cluster, which is extremely vulnerable to future infection, as reported before in [21, 25, 26] .