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We propose a system theoretic approach to select and stabilize the endemic equilibrium of an SIRS epidemic model in which the decisions of a population of strategically interacting agents determine the transmission rate. Specifically, the population's agents recurrently revise their choices out of a set of strategies that impact to varying levels the transmission rate. A payoff vector quantifying the incentives provided by a planner for each strategy, after deducting the strategies' intrinsic costs, influences the revision process. An evolutionary dynamics model captures the population's preferences in the revision process by specifying as a function of the payoff vector the rates at which the agents' choices flow toward strategies with higher payoffs. Our main result is a dynamic payoff mechanism that is guaranteed to steer the epidemic variables (via incentives to the population) to the endemic equilibrium with the smallest infectious fraction, subject to cost constraints. We use a Lyapunov function not only to establish convergence but also to obtain an (anytime) upper bound for the peak size of the population's infectious portion.