Graduate School of Information Sciences, Tohoku University, 6-3-09 Aoba, Aramaki-aza Aoba-ku, Sendai, 980-8579, Miyagi, Japan.
PRESTO, Japan Science and Technology Agency (JST), 4-1-8 Honcho, Kawaguchi, 332-0012, Saitama, Japan.
BMC Infect Dis. 2022 Jun 1;22(1):512. doi: 10.1186/s12879-022-07403-5.
Facing a global epidemic of new infectious diseases such as COVID-19, non-pharmaceutical interventions (NPIs), which reduce transmission rates without medical actions, are being implemented around the world to mitigate spreads. One of the problems in assessing the effects of NPIs is that different NPIs have been implemented at different times based on the situation of each country; therefore, few assumptions can be shared about how the introduction of policies affects the patient population. Mathematical models can contribute to further understanding these phenomena by obtaining analytical solutions as well as numerical simulations.
In this study, an NPI was introduced into the SIR model for a conceptual study of infectious diseases under the condition that the transmission rate was reduced to a fixed value only once within a finite time duration, and its effect was analyzed numerically and theoretically. It was analytically shown that the maximum fraction of infected individuals and the final size could be larger if the intervention starts too early. The analytical results also suggested that more individuals may be infected at the peak of the second wave with a stronger intervention.
This study provides quantitative relationship between the strength of a one-shot intervention and the reduction in the number of patients with no approximation. This suggests the importance of the strength and time of NPIs, although detailed studies are necessary for the implementation of NPIs in complicated real-world environments as the model used in this study is based on various simplifications.
面对 COVID-19 等新传染病的全球流行，全球各地正在实施非药物干预（NPIs）措施，这些措施无需采取医疗措施即可降低传播率，以减轻传播。评估 NPIs 效果的一个问题是，不同的 NPIs 根据每个国家的情况在不同的时间实施；因此，关于政策的引入如何影响患者群体，几乎没有可以共享的假设。数学模型可以通过获得解析解和数值模拟来帮助进一步理解这些现象。
在这项研究中，在 SIR 模型中引入了一种 NPI，以便在仅在有限时间内将传播率降低到固定值一次的情况下对传染病进行概念性研究，并对其进行了数值和理论分析。分析表明，如果干预开始得太早，感染人数的最大比例和最终规模可能会更大。分析结果还表明，随着干预力度的增强，第二次波峰时可能会有更多的人感染。
本研究提供了单次干预的强度与无近似情况下患者数量减少之间的定量关系。这表明 NPIs 的强度和时间很重要，尽管需要对在复杂的现实环境中实施 NPIs 进行详细研究，因为本研究中使用的模型基于各种简化。
