College of Chemistry, University of California, Berkeley, Berkeley, CA, 94720, USA.
Sci Rep. 2021 Oct 14;11(1):20386. doi: 10.1038/s41598-021-99607-z.
Continuous deterministic models have been widely used to guide non-pharmaceutical interventions (NPIs) to combat the spread of the coronavirus disease 2019 (COVID-19). The validity of continuous deterministic models is questionable because they fail to incorporate two important characteristics of human society: high clustering and low degree of separation. A small-world network model is used to study the spread of COVID-19, thus providing more reliable information to provide guidance to mitigate it. Optimal timing of lockdown and reopening society is investigated so that intervention measures to combat COVID-19 can work more efficiently. Several important findings are listed as follows: travel restrictions should be implemented as soon as possible; if 'flattening the curve' is the purpose of the interventions, measures to reduce community transmission need not be very strict so that the lockdown can be sustainable; the fraction of the population that is susceptible, rather than the levels of daily new cases and deaths, is a better criterion to decide when to reopen society; and society can be safely reopened when the susceptible population is still as high as 70%, given that the basic reproduction number is 2.5. Results from small-world network models can be significantly different than those from continuous deterministic models, and the differences are mainly due to a major shortfall intrinsically embedded in the continuous deterministic models. As such, small-world network models provide meaningful improvements over continuous deterministic models and therefore should be used in the mathematical modeling of infection spread to guide the present COVID-19 interventions. For future epidemics, the present framework of mathematical modeling can be a better alternative to continuous deterministic models.
连续确定性模型已被广泛用于指导非药物干预（NPIs）以控制 2019 年冠状病毒病（COVID-19）的传播。由于连续确定性模型未能纳入人类社会的两个重要特征：高聚类和低度分离，因此其有效性值得怀疑。我们使用小世界网络模型来研究 COVID-19 的传播，从而提供更可靠的信息来提供指导以减轻其传播。研究了封锁和重新开放社会的最佳时机，以便对抗 COVID-19 的干预措施能够更有效地发挥作用。以下是一些重要发现：应尽快实施旅行限制；如果“拉平曲线”是干预措施的目的，则减少社区传播的措施不必非常严格，以便封锁能够可持续；决定何时重新开放社会的更好标准是易感人群的比例，而不是每日新发病例和死亡人数的水平；如果基本繁殖数为 2.5，则易感人群仍高达 70%时，社会可以安全地重新开放。小世界网络模型的结果可能与连续确定性模型的结果有很大不同，而差异主要是由于连续确定性模型内在存在的主要缺陷所致。因此，小世界网络模型比连续确定性模型提供了有意义的改进，因此应在感染传播的数学建模中使用，以指导当前的 COVID-19 干预措施。对于未来的流行，本数学建模框架可以是连续确定性模型的更好替代方案。
