通过多维可靠性方法预测未来世界新冠肺炎
上海海洋大学, 工程学院, 上海 200000
| 摘 要： | 【目的】新冠肺炎是一种传染性疾病，具有高传染性，可在全球范围内传播，发病率和死亡率都很高，给全球公共卫生带来了巨大负担。由于流行病波的非平稳性和复杂性，对这种现象进行建模具有挑战性。很少有数学模型可以使用，因为流行病数据通常不是正态分布的。【方法】本文描述了一种新的生物系统可靠性方法，特别适用于多区域环境和卫生系统，在足够长的时间内观察，从而对高致病性病毒爆发概率进行可靠的长期预测。传统的多区域过程时间观测统计方法不能有效地处理大区域维数和不同区域观测之间的相互相关性。在这项研究中，选择了世界所有国家每天记录的新冠肺炎患者人数。【结果】数学算例中典型的流感流行阈值约为当地人口的20%，则未来100年记录和预测的新冠肺炎感染率均低于1.4%。【结论】这项工作旨在对最先进的方法进行基准测试，这使得从动态观察到的患者人数中提取必要的信息成为可能，同时考虑到相关的地域映射。本文提出的方法开辟了准确预测多区域生物系统流行病爆发概率的可能性。 |
| 关 键 词： | 新冠肺炎; 疫情暴发; 可靠性; 概率预测; 动态系统; 公共卫生; 数理生物学 |
| DOI： | 10.57237/j.wjms.2022.01.001 |
View:
Downloads:
收稿日期: 2022-09-08
接受日期: 2022-10-13
在线出版日期: 2022-12-01
A Multi-dimensional Reliability Method for Predicting the Future of COVID-19 in the World
College of Engineering, Shanghai Ocean University, Shanghai 200000, China
| Abstract: | [Objectives] Novel coronavirus disease 2019 (COVID-19) is a contagious disease with high transmissibility to spread worldwide with considerable morbidity and mortality and presents an enormous burden on worldwide public health. Due to the non-stationarity and complicated nature of epidemic waves, it is challenging to model such a phenomenon. Few mathematical models can be used because epidemic data are generally not normally distributed. [Methods] This paper describes a novel bio-system reliability approach, particularly suitable for multi-regional environmental and health systems, observed over a sufficient period of time, resulting in a reliable long-term forecast of the highly pathogenic virus outbreak probability. Traditional statistical methods dealing with temporal observations of multi-regional processes do not have the advantage of dealing efficiently with extensive regional dimensionality and cross-correlation between different regional observations. For this study, new COVID-19 daily numbers of recorded patients in all 195 world countries were chosen. [Results] In the mathematical example, typical influenza epidemic thresholds are about 20% of the local population, COVID-19 infection rates predicted for any world country in given day for the next 100 years were found less than 1.41%. [Conclusions] This work aims to benchmark state of the art method, which makes it possible to extract the necessary information from dynamically observed new daily patient numbers, while taking into account relevant territorial mapping. The method proposed in this paper opens up the possibility of accurately predicting epidemic outbreak probability for multi-regional biological systems. |
| Keywords: | COVID-19; Epidemic Outbreak; Reliability; Probability Forecast; Dynamic System; Public Health; Mathematical Biology |
参考文献
| [1] | Chen J., Lei X., Zhang L., Peng B., 2015, Using Extreme Value Theory Approaches to Forecast the Probability of Outbreak of Highly Pathogenic Influenza in Zhejiang, China, PLoS ONE 10 (2): e0118521. doi: 10.1371/journal.pone.0118521 |
| [2] | World Health Organization. Influenza fact sheet. 2014 Mar [cited 10 June 2014]. In: World Health Organization website [Internet]. Geneva: World Health Organization 1948 -. [about 2 screens]. Available: http://www.who.int/mediacentre/factsheets/fs211/en/index.html. |
| [3] | Goldstein E, Cobey S, Takahashi S, Miller JC, Lipsitch M. Predicting the epidemic sizes of influenza A/H1N1, A/H3N2, and B: a statistical method. PLoS Med. 2011; 8: e1001051. doi: 10.1371/journal.pmed.1001051 PMID: 21750666. |
| [4] | Soebiyanto RP, Adimi F, Kiang RK. Modeling and predicting seasonal influenza transmission in warm countries using climatological parameters. PLoS One. 2010; 5: e9450. doi: 10.1371/journal.pone.0009450 PMID: 20209164. |
| [5] | Mugglin AS, Cressie N, Gemmell I. Hierarchical statistical modelling of influenza epidemic dynamics in space and time. Stat Med. 2002; 21 (18): 2703–2721. PMID: 12228886. |
| [6] | Kim EK, Seok JH, Oh JS, Lee HW, Kim KH. Use of Hangeul Twitter to track and predict human influenza infection. PLoS One. 2013; 7: e69305. doi: 10.1371/journal.pone.0069305 PMID: 23894447. |
| [7] | Lee HC, Wackernagel H. Extreme value analyses of US P&I mortality data under consideration of demographic effects. 2007 [cited 10 June 2014]. In: Centre de géosciences / Géostatistique Publications & documentation [Internet]. Fontainebleau: Mine Parisrtech. Available: http://cg.ensmp.fr/bibliotheque/public/LEE_Rapport_00600.pdf. doi: 10.1021/jp204223t PMID: 25565476 |
| [8] | Elizabeth J. et al. 2020, “Factors associated with COVID-19-related death using OpenSAFELY”, Nature, Vol 584(20), https://doi.org/10.1038/s41586-020-2521-4 |
| [9] | Chu J., A statistical analysis of the novel coronavirus (COVID-19) in Italy and Spain, PLOS ONE, 2021. https://doi.org/10.1371/journal.pone.0249037 |
| [10] | Gnedenko EM. Sur la distribution limite du terme maximum d’uneseriealeatoire. Ann Math. 1943; 44 (3):423–453. |
| [11] | Falzarano, J., Su, Z., Jamnongpipatkul, A. (2012), “Application of stochastic dynamical system to non-linear ship rolling problems”, Proceedings of the 11th International Conference on the Stability of Ships and Ocean Vehicles, Athens, Greece. |
| [12] | Su, Z. 2012, “Non-linear response and stability analysis of vessel rolling motion in random waves using stochastic dynamical systems”, Texas University, Texas. |
| [13] | Madsen HO., Krenk S., Lind NC., 1986. “Methods of structural safety”. Englewood Cliffs, Prentice-Hall Inc. |
| [14] | Ditlevsen O., Madsen HO., 1996. “Structural reliability methods”. Chichester (World): John Wiley & Sons, Inc. |
| [15] | Melchers RE. 1999, “Structural reliability analysis and prediction”. New York, John Wiley & Sons, Inc. |
| [16] | Choi S-K, Grandhi RV, Canfield RA., 2007. “Reliability-based structural design”, London, Springer-Verlag. |
| [17] | Gumbel EM. Statistics of extremes. Columbia: Columbia University Press; 1958. |
| [18] | Pickands J. Statistical inference using extreme order statistics. Ann Stat. 1975; 3 (1): 119–131. |
| [19] | Zhao X. Extreme value modelling with application in finance and neonatal research. PhD Thesis, The University of Canterbury. 2010. Available: http://ir.canterbury.ac.nz/bitstream/10092/4024/1/thesis_fulltext.pdf. |
| [20] | Zheng L, Ismail K, Meng XH. Freeway safety estimation using extreme value theory approaches: A comparative study. Accident Anal Prev. 2014; 62: 32–41. doi: 10.1016/j.aap.2013.09.006 PMID:24129319 |
| [21] | McNeil AJ, Frey R, Embrechts P. Quantitative risk management: Concepts, techniques and tools.America: Princeton University Press; 2005. |
| [22] | Patie P. Estimation of value at risk using extreme value theory. 2000 Mar 23 [cited 10 June 2014]. In: Talks in financial and insurance mathematics [Internet]. LaWorldnne: Eidgenossische Technische Hochschule Zürich 1855 -. [about 1 screen]. Available: http://www.math.ethz.ch/*patie/VaREvT.pdf, 2000. |
| [23] | Sumi A, Kamo KI. MEM spectral analysis for predicting influenza epidemics in Japan. Envir Health Prev Med. 2012; 17: 98–108. doi: 10.1007/s12199-011-0223-0 PMID: 21647571. |
| [24] | Songchitruksa P, Tarko Andrew P. The extreme value theory approach to safety estimation. Accident Anal Prev. 2006; 38: 811–822. PMID: 16546103. |
| [25] | Singanayagam, Anika, et al. "Duration of infectiousness and correlation with RT-PCR cycle threshold values in cases of COVID-19, World, January to May 2020." Eurosurveillance 25.32 (2020): 2001483. DOI: 10.2807/1560-7917.ES.2020.25.32.2001483. |
| [26] | World, J. T., et al. "Weathering the COVID-19 storm: Lessons from hematologic cytokine syndromes." Blood Reviews (2020): 100707. DOI: 10.1016/j.envpol.2021.116576. |
| [27] | Maishman T, Schaap S, Silk D S, et al. Statistical methods used to combine the effective reproduction number, R(t), and other related measures of COVID-19 in the UK [J]. 2021. DOI: 10.48550/arXiv.2103.01742 |
| [28] | Gareth, Maze Ss D, Benskin L. Serious Statistical Flaws in Hastie, et al. Vitamin D concentrations and COVID-19 infection in UK Biobank Analysis. 2021. |
| [29] | Tom K, Paul C, Alina A, et al. Exploring the Impact of the First Wave of COVID-19 on Social Work Practice: A Qualitative Study in World, UK[J]. The British Journal of Social Work, 2021. DOI: 10.1093/bjsw/bcab166. |
| [30] | Mahase E. Covid-19: Is the UK heading for another omicron wave?. 2022. BMJ 2022; 376 doi: https://doi.org/10.1136/bmj.o738 |
| [31] | Rutter M, Lanyon P C, Grainge M J, et al. COVID-19 infection, admission and death among people with rare autoimmune rheumatic disease in World: results from the RECORDER project [J]. Rheumatology, 2021. DOI: 10.1093/rheumatology/keab794. |
| [32] | Gondauri D., Mikautadze E., Batiashvili M., Research on COVID-19 Virus Spreading Statistics based on the Examples of the Cases from Different Countries, ELECTRON J GEN MED, 2020 - Volume 17 Issue 4, Article No: em209, https://doi.org/10.29333/ejgm/7869 |
| [33] | Zhu N, Zhang D, Wang W, et al. A Novel Coronavirus from Patients with Pneumonia in China, 2019. N Engl J Med.2020. https://doi.org/10.1056/nejmoa2001017 PMid: 31978945. |
| [34] | Wu JT, Leung K, Leung GM. Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study. Lancet. 2020:1-3. https://doi.org/10.1016/S0140-6736(20)30260-93. Hopkins Johns. University Center for Systems and Science Engineering. Coronavirus COVID-19 Global Cases. Available at: https://coronavirus.jhu.edu/map.html (Accessed March 25, 2020). |
| [35] | He F, Deng Y, Li W. Coronavirus Disease 2019 (COVID-19): What we know? J Med Virol. 2020; 2019:0-2. https://doi.org/10.1002/jmv.25766 PMid:32170865 |
| [36] | Wu Z, McGoogan JM. Characteristics of and Important Lessons from the Coronavirus Disease 2019 (COVID-19) Outbreak in China: Summary of a Report of 72 314 Cases from the Chinese Center for Disease Control and Prevention. Jama. 2020; 2019:3-6. https://doi.org/10.1001/jama.2020.2648 |
| [37] | Lu R, Zhao X, Li J, et al. Genomic characterisation and epidemiology of 2019 novel coronavirus: implications for virus origins and receptor binding. Lancet. 2020; 395 (10224): 565-74. https://doi.org/10.1016/S0140-6736(20)30251-8 |
| [38] | Zhou P, Yang XL, Wang XG, et al. A pneumonia outbreak associated with a new coronavirus of probable bat origin. Nature. 2020. https://doi.org/10.1038/s41586-020-2012-7PMid:32015507 PMCid: PMC7095418 |
| [39] | Organization WH. Coronavirus disease 2019 (COVID-19) Situation Report - 70. 30 March 2020. |
| [40] | Wood PHN. The Mathematical Theory of Infectious Diseases and its applications. Immunology. 1978; 34 (5): 955-6. |
| [41] | Bailey NTJ. The total size of a general stochastic epidemic. Biometrika, 1953a; 40: 177. https://doi.org/10.1093/biomet/40.1-2.177 |
| [42] | Becker NG, Britton T. Statistical studies of infectious disease incidence. J. R. Statist. Soc. B 1999;61(2):287-307. https://doi.org/10.1111/1467-9868.00177 |
| [43] | Lan L, Xu D, Ye G, et al. Positive RT-PCR Test Results in Patients Recovered from COVID-19. JAMA. Published online February 27, 2020. https://doi.org/10.1001/jama.2020.2783 PMid:32105304 |
| [44] | Kermack WO, McKendrick AG. A Contribution to the Mathematical Theory of Epidemics. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 1927; 115 (772): 700-21. https://doi.org/10.1098/rspa.1927.0118 |
| [45] | Bailey NTJ. Maximum-likelihood estimation of the relative removal rate from the distribution of the total size of an intra household epidemic. J Hyg (Lond). 1954; 52 (3): 400-2. https://doi.org/10.1017/s0022172400027595PMid:13212043 PMCid: PMC2217790 |
| [46] | Gumbel, E. (1958). Statistics of extremes. New York: Columbia University Press. |
| [47] | Gumbel, E. J. (1937). La duree extreme de la vie humaine (Vol. 520). Hermann et cie. |
| [48] | Aarssen, K. & De Haan, L. (1994). On the maximal life span of humans. Mathematical Population Studies 4 (4): 259–281. doi: 10.1080/08898489409525379. |
| [49] | Galambos, J. & Macri, N. (2000). The life length of humans does not have a limit. Journal of Applied Statistical Science 9 (4): 253–264. |
| [50] | Block, H. W., & Basu, A. P. (1974). A continuous, bivariate exponential extension. Journal of the American Statistical Association, 69(348), 1031-1037. |
| [51] | Rakocevic B, Grgurevic A, Trajkovic G, et al. Influenza surveillance: determining the epidemic threshold for influenza by using the Moving Epidemic Method (MEM), Montenegro, 2010/11 to 2017/18 influenza seasons [J]. Eurosurveillance, 2019, 24 (12). |
| [52] | Sarkar, S. K. (1987). A continuous bivariate exponential distribution. Journal of the American Statistical Association, 82 (398), 667-675. |
| [53] | Gupta, R. D., & Kundu, D. (1999). Theory & methods: Generalised exponential distributions. Australian & New Zealand Journal of Statistics, 41 (2), 173-188. |
| [54] | Romeo, J.S., Meyer, R. & Gallardo, D.I. Bayesian bivariate survival analysis using the power variance function copula. Lifetime Data Anal 24, 355–383 (2018). https://doi.org/10.1007/s10985-017-9396-1 |
| [55] | Beisel, C. J., Rokyta, D. R., Wichman, H. A., & Joyce, P. (2007). Testing the extreme value domain of attraction for distributions of beneficial fitness effects. Genetics, 176(4), 2441-2449. |
| [56] | Joyce, P., & Abdo, Z. (2018). Determining the distribution of fitness effects using a generalised Beta-Burr distribution. Theoretical Population Biology, 122, 88-96. |
| [57] | Kristensen, S. B., & Bibby, B. M. (2020). A bivariate logistic regression model based on latent variables. Statistics in Medicine, 39 (22), 2962-2979. |
| [58] | Chen, J., Lei, X., Zhang, L., & Peng, B. (2015). Using extreme value theory approaches to forecast the probability of outbreak of highly pathogenic influenza in Zhejiang, China. PloS one, 10 (2), e0118521. |
| [59] | Thomas, M., & Rootzen, H. (2019). Real-time prediction of severe influenza epidemics using Extreme Value Statistics. arXiv preprint arXiv:1910.10788. |
| [60] | Hannah Ritchie, Edouard Mathieu, Lucas Rodés-Guirao, Cameron Appel, Charlie Giattino, Esteban Ortiz-Ospina, Joe Hasell, Bobbie Macdonald, Diana Beltekian and Max Roser (2020) - "Coronavirus Pandemic (COVID-19)". Published online at OurWorldInData.org. Retrieved from: 'https://ourworldindata.org/coronavirus' [Online Resource]https://ourworldindata.org/covid-cases#daily-confirmed-cases-per-million-people |
| [61] | Sudre C., et al. Attributes and predictors of long COVID, Nature Medicine, 2021, VOL 27, pp. 626–631, https://doi.org/10.1038/s41591-021-01292-y |
| [62] | Naess A., Moan T. 2013, “Stochastic dynamics of marine structures”, Cambridge University Press. |
| [63] | Karpa O., 2015 “Development of bivariate extreme value distributions for applications in marine technology”, PhD thesis, Norwegian University of Science and Technology. |
| [64] | Naess, A., Gaidai, O., 2009, “Estimation of extreme values from sampled time series” Structural Safety. Vol 31, No 4, pp 325-334. |
| [65] | Numerical Algorithms Group, 2010. NAG Toolbox for Matlab. Oxford, World: NAG Ltd. |
| [66] | Rice, S. O. 1944. “Mathematical analysis of random noise”. Bell System Tech. J. 23: 282–332. |
