The coronavirus disease (COVID-19) has infected more than 79 million individuals, with 1.7 million deaths worldwide. Several countries have implemented social distancing and testing policies with contact tracing as a measure to flatten the curve of the ongoing pandemic. Optimizing these control measures is urgent given the substantial societal and economic impacts associated with infection and interventions. To determine the optimal social distancing and testing strategies, we developed a mathematical model of COVID-19 transmission and applied optimal control theory, identifying the best approach to reduce the epidemiological burden of COVID-19 at a minimal cost. The results demonstrate that testing as a standalone optimal strategy does not have a significant effect on the final size of an epidemic, but it would delay the peak of the pandemic. If social distancing is the sole control strategy, it would be optimal to gradually increase the level of social distancing as the incidence curve of COVID-19 grows, and relax the measures after the curve has reached its peak. Compared with a single strategy, combined social distancing and testing strategies are demonstrated to be more efficient at reducing the disease burden, and they can delay the peak of the disease. To optimize these strategies, testing should be maintained at a maximum level in the early phases and after the peak of the epidemic, whereas social distancing should be intensified when the prevalence of the disease is greater than 15%. Accordingly, public health agencies should implement early testing and switch to social distancing when the incidence level begins to increase. After the peak of the pandemic, it would be optimal to gradually relax social distancing and switch back to testing.

冠状病毒病 (COVID-19) 已感染超过 7900 万人，全球有 170 万人死亡。一些国家已经实施了社会疏远和检测政策，并进行了接触者追踪，作为压平当前大流行曲线的措施。鉴于与感染和干预措施相关的巨大社会和经济影响，优化这些控制措施刻不容缓。为了确定最佳的社交距离和检测策略，我们开发了 COVID-19 传播的数学模型，并应用最优控制理论，确定了以最低成本减少 COVID-19 流行病学负担的最佳方法。结果表明，作为独立的最佳策略进行测试不会对流行病的最终规模产生重大影响，但会推迟流行病的高峰期。如果社交距离是唯一的控制策略，那么最好是随着COVID-19发病率曲线的增长逐渐提高社交距离水平，并在曲线达到峰值后放松措施。与单一策略相比，社会疏远和检测相结合的策略被证明可以更有效地减轻疾病负担，并且可以推迟疾病的高峰期。为了优化这些策略，应在疫情早期和高峰期后维持最高水平的检测，而当疾病患病率大于15%时应加强社交距离。因此，公共卫生机构应尽早实施检测，并在发病率开始上升时转向保持社交距离。疫情高峰期过后，最好是逐步放宽社交距离，重新进行检测。