  We study a behavioral SIR model with time-varying costs of distancing. The
two main causes of the variation in the cost of distancing we explore are
distancing fatigue and public policies (lockdowns). We show that for a second
wave of an epidemic to arise, a steep increase in distancing cost is necessary.
Distancing fatigue cannot increase the distancing cost sufficiently fast to
create a second wave. However, public policies that discontinuously affect the
distancing cost can create a second wave. With that in mind, we characterize
the largest change in the distancing cost (due to, for example, lifting a
public policy) that will not cause a second wave. Finally, we provide a
numerical analysis of public policies under distancing fatigue and show that a
strict lockdown at the beginning of an epidemic (as, for example, recently in
China) can lead to unintended adverse consequences. When the policy is lifted
the disease spreads very fast due to the accumulated distancing fatigue of the
individuals causing high prevalence levels.
