An epidemiological evolutionary game model with regulation

We propose a coevolutionary model linking epidemic dynamics to the strategic choices of agents, in response to decisions by a central regulator. The epidemic is represented by a discrete-time SIS model, with the infection rate endogenously determined by agent strategies. In particular, cooperative and non-cooperative behaviors correspond to low and high infection rates, respectively, and the overall rate is a weighted average based on the population shares adopting each strategy. These shares change with time through an evolutionary selection mechanism, whose fitness measure depends on the epidemic trajectory relative to the agent perceived alert threshold, above which the epidemic situation is considered risky by agents. The regulator influences the alert level based on an ideal target number of infections. The model, describing the evolution of the epidemiological sector, of the share updating rule and of the alert threshold, consists of a three-dimensional discrete-time system. We study the resulting interplay both from a static perspective, focusing in particular on the nature of the strategic interaction at both endemic and disease-free steady states, as well as in regard to dynamical features, taking into account out-of-equilibrium trajectories and investigating the possible emergence of multistability phenomena.