An epidemic spreading in a network calls for a decision on the part of the network members: They should decide whether to protect themselves or not. Their decision depends on the trade off between their perceived risk of being infected and the cost of being protected. The network members can make decisions repeatedly, based on information that they receive about the changing infection level in the network. We study the equilibrium states reached by a network whose members increase (resp. decrease) their security deployment when learning that the network infection is higher (resp. lower). Our main result is that as the learning rate of the members increases, the equilibrium level of infection increases. We demonstrate this result both when members are strictly rational and when they are not. We characterize the domains of attraction of the equilibrium points. We validate our conclusions with simulations on human mobility traces.