[论文解读] A simple iterative map forecast of the COVID-19 pandemic

Botha Ae, W. Dednam|arXiv (Cornell University)|Mar 23, 2020

COVID-19 epidemiological studies参考文献 11被引用 12

一句话总结

本文提出一个仅含两个拟合参数的简单三维迭代映射模型，利用世卫组织提供的累计与新增病例数据，预测全球COVID-19的传播情况。该模型捕捉了由于实施封锁措施而导致的从指数增长向幂律增长的转变，预测在无干预情况下，每日新增病例峰值将达到约6000万例，出现在第133天（2020年5月中旬），但表明持续封锁可推迟该峰值，并通过长期受控传播减缓传播速度。

ABSTRACT

We develop a simple 3-dimensional iterative map model to forecast the global spread of the coronavirus disease. Our model contains at most two fitting parameters, which we determine from the data supplied by the world health organisation for the total number of cases and new cases each day. We find that our model provides a surprisingly good fit to the currently-available data, which exhibits a cross-over from exponential to power-law growth, as lock-down measures begin to take effect. Before these measures, our model predicts exponential growth from day 30 to 69, starting from the date on which the world health organisation provided the first `Situation report' (21 January 2020 $-$ day 1). Based on this initial data the disease may be expected to infect approximately 23% of the global population, i.e. about 1.76 billion people, taking approximately 83 million lives. Under this scenario, the global number of new cases is predicted to peak on day 133 (about the middle of May 2020), with an estimated 60 million new cases per day. If current lock-down measures can be maintained, our model predicts power law growth from day 69 onward. Such growth is comparatively slow and would have to continue for several decades before a sufficient number of people (at least 23% of the global population) have developed immunity to the disease through being infected. Lock-down measures appear to be very effective in postponing the unimaginably large peak in the daily number of new cases that would occur in the absence of any interventions. However, should these measure be relaxed, the spread of the disease will most likely revert back to its original exponential growth pattern. As such, the duration and severity of the lock-down measures should be carefully timed against their potentially devastating impact on the world economy.

研究动机与目标

• 开发一种基于公开数据的最小参数模型，用于预测全球COVID-19的传播情况。
• 捕捉由于干预措施影响导致的病例数从指数增长向幂律增长的转变。
• 在无干预与持续封锁条件下，估算大流行可能的规模。
• 评估封锁持续时间对病例峰值及全球免疫阈值的长期影响。

提出的方法

• 该模型使用一个包含两个可调参数的三维迭代映射，基于世卫组织报告的每日累计与新增病例数进行拟合。
• 它将封锁措施实施前的指数增长（第69天之前）与实施后的幂律增长（从第69天起）的转变进行建模。
• 模型的动力学由代表累计病例数、新增病例数及增长调节因子的状态变量的迭代更新所驱动。
• 参数拟合使用从2020年1月21日（第1天）世卫组织首份《疫情报告》至分析时刻的数据完成。
• 该模型假设从指数增长向幂律增长的转变反映了非药物干预措施（如社交距离）的影响。
• 通过在持续封锁条件下模拟模型，预测长期结果，假设幂律增长将持续。

实验结果

研究问题

• RQ1 若不采取任何干预措施，全球COVID-19病例的预测轨迹如何？
• RQ2 封锁措施如何改变新增病例的增长模式？在这些条件下，峰值预计出现在何时？
• RQ3 在无干预情景下，预测的全球感染率和总死亡人数是多少？
• RQ4 持续封锁需要持续多长时间，才能通过自然感染实现足够的群体免疫？
• RQ5 长期封锁与医疗系统超载风险之间的经济权衡是什么？

主要发现

• 在无干预情况下，模型预测从第30天到第69天为指数增长，导致约17.6亿例感染（占全球人口的23%）。
• 在无干预情景下，模型预测在第133天（2020年5月中旬）达到每日新增病例约6000万例的峰值。
• 从第69天起，由于封锁措施的实施，模型预测将出现向幂律增长的转变，表明传播速度显著减缓。
• 在持续封锁条件下，幂律增长将持续数十年，直至达到23%的免疫阈值。
• 模型表明，若放松封锁，传播很可能重新转为指数增长，导致病例再次激增。
• 结果表明，封锁措施在推迟峰值方面极为有效，但需精心把握时机，以平衡公共卫生与经济影响。