临界慢化理论在传染病免疫消除过程中的应用

周芮; 王雪晴; 赵继军

doi:10.13306/j.1672-3813.2026.02.019

复杂系统与复杂性科学 >

2026 , Vol. 23 >Issue 2: 152 - 158

DOI: https://doi.org/10.13306/j.1672-3813.2026.02.019

研究前沿

临界慢化理论在传染病免疫消除过程中的应用

周芮 ,
王雪晴 ,
赵继军

展开

青岛大学复杂性科学研究所,山东青岛 266071

周芮(1998-),女,江西宜春人,硕士研究生,主要研究方向为流行病学动态特性。

收稿日期: 2023-10-31

修回日期: 2024-02-01

网络出版日期: 2026-05-19

基金资助

山东省自然科学基金(ZR2018MH037)

收起

Application of Critical Slowing Downing Theory in Anticipating Infections Disease Elimination

ZHOU Rui ,
WANG Xueqing ,
ZHAO Jijun

Expand

Institute of Complex Science, Qingdao University, Qingdao 266071, China

Received date: 2023-10-31

Revised date: 2024-02-01

Online published: 2026-05-19

Fold

摘要

临界慢化理论中的早期预警信号(Early Warning Signal, EWS)可以预测传染病消除过程的阈值,为消除计划提供科学指导。应用SIR随机模型进行多次仿真,用得到的发病数据计算EWS的曲线下面积,以此评估EWS区分的效果。结果发现:EWS在初始免疫高水平下仍然有效,但效果较初始免疫率为0的情况有所减弱;均值和方差对发病数下降的系统敏感,而变异系数不仅稳健,还在系统靠近和远离转换点上的区分效果优秀;自协相关、自相关和衰减时间随时间上升是系统靠近转换点的信号。

关键词： 临界慢化理论; 早期预警信号; 曲线下面积; 传染病消除

本文引用格式

周芮 , 王雪晴 , 赵继军 . 临界慢化理论在传染病免疫消除过程中的应用[J]. 复杂系统与复杂性科学, 2026 , 23(2) : 152 -158 . DOI: 10.13306/j.1672-3813.2026.02.019

Abstract

Early warning signals (EWS) from the theory of critical slowing down can anticipate the threshold of disease elimination process and provide scientific guidance for disease elimination plans. In this paper, we consider the SIR stochastic model with multiple simulations for incidence data and calculate the area under the curve to evaluate the effect of EWS behaviors. We find that EWS remains effective even at high initial levels of immunity, although its effectiveness diminishes compared to scenarios where the initial immunity rate is zero. Mean and variance are sensitive to the system with a decrease in the number of cases, while the coefficient of variation is not only robust but also exhibits excellent discriminatory effects as the system approaches or moves away from the tipping point. Autocovariance, lag-1 autocorrelation and decay time increase before the system approach to the tipping point.

Key words： critical slowing down theory; early warning signals; area under the curve; disease elimination

参考文献

[1] FENNER F, HENDERSON D A, ARITA I, et al. Smallpox and Its Eradication[M]. Washington D C: Congressional Information Service Inc, 1988.
[2] 杨维中,贾萌萌. 中国消除传染病的历史进程与展望[J]. 中华流行病学杂志, 2021, 42(11): 1907-1911.
YANG W Z, JIA M M. Elimination of infectious disease in China, past and future[J]. Chinese Journal of Epidemiology, 2021, 42(11): 1907-1911.
[3] DRAKE J M, HAY S I. Monitoring the path to the elimination of infectious diseases[J]. Tropical Medicine and Infectious Disease, 2017, 2(3): 20.
[4] 徐驰,王海军,刘权兴,等. 生态系统的多稳态与突变[J]. 生物多样性, 2020, 28(11): 1417-1430.
XU C, WANG H J, LIU Q X, et al. Alternative stable states and tipping points of ecosystems[J]. Biodiversity Science, 2020, 28(11): 1417-1430.
[5] SCHEFFER M, BASCOMPTE J, BROCK W A, et al. Early-warning signals for critical transitions[J]. Nature, 2009, 461: 53-59.
[6] SOUTHALL E, BRETT T S, TILDESLEY M J, et al. Early warning signals of infectious disease transitions: a review[J]. Journal of The Royal Society Interface, 2021, 18(182): 20210555.
[7] SCHEFFER M, BASCOMPTE J, BROCK W A, et al. 临界转换的早期预警信号[J]. 国际地震动态, 2009(9): 1-14.
SCHEFFER M, BASCOMPTE J, BROCK W A, et al. Early warning signal of critical transition[J]. Recent Developments in World Seidmology, 2009(9): 1-14.
[8] 尹彩春,赵文武,李琰,等. 气候系统中临界转变的研究进展与展望[J]. 地球科学进展, 2021,36(12): 1313-1323.
YIN C C, ZHAO W W, LI Y, et al. Critical transitions in the climate system: progress and prospect[J]. Advances in Earth Science, 2021, 36(12): 1313-1323.
[9] 苏小芸,陈丽君,王文才,等. 甘东南地区水氡浓度的临界慢化现象研究[J]. 地震工程学报, 2020,42(5): 1104-1110,1140.
SU X Y, CHEN L J, WANG W C, et al. Critical-slowing-down phenomenon of water radon concentration in the Southeastern Gansu Region[J]. China Earthquake Engineering Journal, 2020,42(5): 1104-1110,1140.
[10] DRAKE J M, GRIFFEN B D. Early warning signals of extinction in deteriorating environments[J]. Nature, 2010, 467(7314): 456-459.
[11] O’REGAN S M, DRAKE J M. Theory of early warning signals of disease emergence and leading indicators of elimination[J]. Theoretical Ecology, 2013, 6(3): 333-357.
[12] HARRIS M J, HAY S I, DRAKE J M. Early warning signals of malaria resurgence in Kericho, Kenya[J]. Biology Letters, 2020, 16(3): 20190713.
[13] SOUTHALL E, TILDESLEY M J, DYSON L. Prospects for detecting early warning signals in discrete event sequence data: application to epidemiological incidence data[J]. PLOS Computational Biology, 2020, 16(9): e1007836.
[14] DRAKE J M, BRETT T S, CHEN S, et al. The statistics of epidemic transitions[J]. PLOS Computational Biology, 2019, 15(5): e1006917.
[15] 山东省统计局.山东统计年鉴[M].北京:中国统计出版社,2023.
[16] 周武略. 麻疹在中国的空间传播[D]. 青岛:青岛大学,2021.
ZHOU W L. Space transmission of measles in China[D]. Qingdao: Qingdao University, 2021.
[17] PATEL M K, GOODSON J L, ALEXANDER J P, et al. Progress toward regional measles elimination-worldwide, 2000—2019[J]. Morbidity and Mortality Weekly Report, 2020, 69(45): 1700-1705.
[18] YANG W, LI J, SHAMAN J. Characteristics of measles epidemics in China (1951—2004) and implications for elimination: a case study of three key locations[J]. PLOS Computational Biology, 2019, 15(2): e1006806.
[19] O’DEA E. Getting started with spaero[EB/OL]. (2020-09-26)[2023-10-29]. https://cran.r-project.org/web/packages/spaero/index.html.
[20] BRETT T S, O’DEA E B, MARTY É, et al. Anticipating epidemic transitions with imperfect data[J]. PLOS Computational Biology, 2018, 14(6): e1006204.
[21] O’REGAN S M, LILLIE J W, DRAKE J M. Leading indicators of mosquito-borne disease elimination[J]. Theoretical Ecology, 2016, 9(3): 269-286.
[22] KENDALL M G. A new measure of rank correlation[J]. Biometrika, 1938, 30(1/2): 81-93.
[23] MILLER P B, O’DEA E B, ROHANI P, et al. Forecasting infectious disease emergence subject to seasonal forcing[J]. Theoretical Biology and Medical Modelling, 2017, 14(1): 17.
[24] FAWCETT T. An introduction to ROC analysis[J]. Pattern Recognition Letters, 2006, 27(8): 861-874.
[25] BRETT T S, ROHANI P. Dynamical footprints enable detection of disease emergence[J]. PLOS Biology, 2020, 18(5): e3000697.
[26] 张明东, 李科赞. 一类具有社团结构的传播网络的阈值分析[J]. 桂林电子科技大学学报, 2014,34(6): 494-502.
ZHANG M D, LI K Z. Threshold analysis of a spreading network with community structure[J]. Journal of Guilin University of Electronic Technology, 2014,34(6): 494-502.

Options

文章导航

模态框（Modal）标题

摘要

本文引用格式

Abstract

参考文献