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.
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