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

Coevolution of agents and networks in an epidemiological model