Stabilizing the return to normal behavior in an epidemic.

Predicting the interplay between behavior and infectious disease has been an intractable problem because response can be so varied. We introduce a general framework for feedback between incidence and behavior in an epidemic. By identifying stable equilibria, we provide policy end-states that are self-managing and self-maintaining. We show that the classical vaccination threshold for eliminating a disease is robust for any behavioral feedback. We prove that without vaccination there is a new endemic incidence level that is dependent on reduced behavior. Between these extremes, we discover a new endemic equilibrium that allows a return to normal behavior and can be stabilized with a lower level of vaccination than required for disease elimination. This framework allows us to anticipate the long term consequence of an emerging disease and design a vaccination response that optimizes public health and limits societal consequences.