  We analyze an optimal control version of a simple SIRS epidemiology model.
The policy maker can adopt policies to diminish the contact rate between
infected and susceptible individuals, at a specific economic cost. The arrival
of a vaccine will immediately end the epidemic. Total or partial immunity is
modeled, while the contact rate can exhibit a (user specified) seasonality. The
problem is solved in a spreadsheet environment. A reasonable parameter
selection leads to optimal policies which are similar to those followed by
different countries. A mild response relying on eventually reaching a high
immunity level is optimal if ample health facilities are available. On the
other hand limited health care facilities lead to strict lock downs while
moderate ones allow a flattening of the curve approach.
