  Motivated by COVID-19, we develop and analyze a simple stochastic model for a
disease spread in human population. We track how the number of infected and
critically ill people develops over time in order to estimate the demand that
is imposed on the hospital system. To keep this demand under control, we
consider a class of simple policies for slowing down and reopening the society
and we compare their efficiency in mitigating the spread of the virus from
several different points of view. We find that in order to avoid overwhelming
of the hospital system, a policy must impose a harsh lockdown or it must react
swiftly (or both). While reacting swiftly is universally beneficial, being
harsh pays off only when the country is patient about reopening and when the
neighboring countries coordinate their mitigation efforts. Our work highlights
the importance of acting decisively when closing down and the importance of
patience and coordination between neighboring countries when reopening.
