Equilibrium social activity during an epidemic

During an infectious-disease epidemic, people make choices that impact transmission, trading off the risk of infection with the social-economic benefits of activity. We investigate how the qualitative features of an epidemic's Nash-equilibrium trajectory depend on the nature of the economic benefits that people get from activity. If economic benefits do not depend on how many others are active, as usually modeled, then there is a unique equilibrium trajectory, the epidemic eventually reaches a steady state, and agents born into the steady state have zero expected lifetime welfare. On the other hand, if the benefit of activity increases as others are more active (“social benefits”) and the disease is sufficiently severe, then there are always multiple equilibrium trajectories, including some that never settle into a steady state and that welfare dominate any given steady-state equilibrium. Within this framework, we analyze the equilibrium impact of a policy that modestly reduces the transmission rate. Such a policy has no long-run effect on society-wide welfare absent social benefits, but can raise long-run welfare if there are social benefits and the epidemic never settles into a steady state.