  We study the spreading of an infection within an SIS epidemiological model on
a network. Susceptible agents are given the opportunity of breaking their links
with infected agents, and reconnecting those links with the rest of the
population. Thus, the network coevolves with the population as the infection
progresses. We show that a moderate reconnection frequency is enough to
completely suppress the infection. A partial, rather weak isolation of infected
agents suffices to eliminate the endemic state.
