  We analyze 'stop and go' containment policies which produces infection cycles
as periods of tight lock-downs are followed by periods of falling infection
rates, which then lead to a relaxation of containment measures, allowing cases
to increase again until another lock-down is imposed. The policies followed by
several European countries seem to fit this pattern. We show that 'stop and go'
should lead to lower medical costs than keeping infections at the midpoint
between the highs and lows produced by 'stop and go'. Increasing the upper and
reducing the lower limits of a stop and go policy by the same amount would
lower the average medical load. But increasing the upper and lowering the lower
limit while keeping the geometric average constant would have the opposite
impact. We also show that with economic costs proportional to containment, any
path that brings infections back to the original level (technically a closed
cycle) has the same overall economic cost.
