  In this paper, we investigate game-theoretic strategies for containing
spreading processes on large-scale networks. Specifically, we consider the
class of networked susceptible-infected-susceptible (SIS) epidemics where a
large population of agents strategically choose whether to adopt partially
effective protection. We define the utilities of the agents which depends on
the degree of the agent, its individual infection status and action, as well as
the the overall prevalence of the epidemic and strategy profile of the entire
population. We further present the coupled dynamics of epidemic evolution as
well as strategy update which is assumed to follow the replicator dynamics. By
relying on timescale separation arguments, we first derive the optimal strategy
of protection adoption by the agents for a given epidemic state, and then
present the reduced epidemic dynamics. The existence and uniqueness of endemic
equilibrium is rigorously characterized and forms the main result of this
paper. Finally, we present extensive numerical results to highlight the impacts
of heterogeneous node degrees, infection rates, cost of protection adoption,
and effectiveness of protection on the epidemic prevalence at the equilibrium.
