  The rapid spread of the Coronavirus (COVID-19) confronts policy makers with
the problem of measuring the effectiveness of containment strategies, balancing
public health considerations with the economic costs of social distancing
measures. We introduce a modified epidemic model that we name the
controlled-SIR model, in which the disease reproduction rate evolves
dynamically in response to political and societal reactions. An analytic
solution is presented. The model reproduces official COVID-19 cases counts of a
large number of regions and countries that surpassed the first peak of the
outbreak. A single unbiased feedback parameter is extracted from field data and
used to formulate an index that measures the efficiency of containment
strategies (the CEI index). CEI values for a range of countries are given. For
two variants of the controlled-SIR model, detailed estimates of the total
medical and socio-economic costs are evaluated over the entire course of the
epidemic. Costs comprise medical care cost, the economic cost of social
distancing, as well as the economic value of lives saved. Under plausible
parameters, strict measures fare better than a hands-off policy. Strategies
based on current case numbers lead to substantially higher total costs than
strategies based on the overall history of the epidemic.
