A two-level policy for controlling an epidemic and its dynamics

Governments and organizations must implement appropriate countermeasures at proper times to control an epidemic and its dynamics. This paper provides a framework for implementing both constant and temporary countermeasures. We show that imposing constant countermeasures (e.g., wearing face masks and keeping social distances till the end of an epidemic cycle) will reduce the total size, and the earlier the more total size reduction. We should implement constant countermeasures as early as possible. Next, temporary countermeasures (e.g., closing businesses in a short period) can always reduce the total size. But implementing temporary countermeasures earlier does not necessarily reduce the total size more. Rather, we should carry out temporary countermeasures around when infectious are high. Based on empirical data and analytical models, we then present a 2-level control policy for restraining infectious peaks and for reducing the total size. The upper control level is a target we try to curb the current infectious below, whereas the lower control level is when we switch back to normal. A tighter control level requires longer closing periods with a more total size reduction, but the total size reduction per closing period becomes less. Implementing a heavier temporary countermeasure (e.g., lockdown vs. only school closing) does not always reduce the total size more because the infectious will bounce back higher when reopen. Dynamic lax-tight policies (lax control early and tight control late) are better than their corresponding tight-lax policies. The crucial reason is a tailing effect: higher infectious lingering around in the late stages.