SCIENCE CHINA Information Sciences, Volume 63 , Issue 12 : 222203(2020) https://doi.org/10.1007/s11432-020-3034-y

Prediction of COVID-19 spread by sliding mSEIR observer

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  • ReceivedMar 12, 2020
  • AcceptedAug 1, 2020
  • PublishedNov 12, 2020



This work was supported by Fundamental Research Funds for the Central Universities (Grant No. 2242019K40111), National Natural Science Foundation of China (Grant Nos. 61903079, 61673107), and Jiangsu Provincial Key Laboratory of Networked Collective Intelligence (Grant No. BM2017002).


[1] Merrell D S, Butler S M, Qadri F. Host-induced epidemic spread of the cholera bacterium. Nature, 2002, 417: 642-645 CrossRef ADS Google Scholar

[2] Lopman B, Vennema H, Kohli E. Increase in viral gastroenteritis outbreaks in Europe and epidemic spread of new norovirus variant. Lancet, 2004, 363: 682-688 CrossRef Google Scholar

[3] Newman M E J. Spread of epidemic disease on networks. Phys Rev E, 2002, 66: 016128 CrossRef ADS arXiv Google Scholar

[4] Barthélemy M, Barrat A, Pastor-Satorras R. Velocity and Hierarchical Spread of Epidemic Outbreaks in Scale-Free Networks. Phys Rev Lett, 2004, 92: 178701 CrossRef ADS arXiv Google Scholar

[5] Gang Y, Tao Z, Jie W. Epidemic Spread in Weighted Scale-Free Networks. Chin Phys Lett, 2005, 22: 510-513 CrossRef ADS arXiv Google Scholar

[6] Keeling M J, Eames K T D. Networks and epidemic models. J R Soc Interface, 2005, 2: 295-307 CrossRef Google Scholar

[7] Lee H W, Malik N, Shi F. Social clustering in epidemic spread on coevolving networks. Phys Rev E, 2019, 99: 062301 CrossRef ADS Google Scholar

[8] Wang G, Hendon H H, Arblaster J M. Compounding tropical and stratospheric forcing of the record low Antarctic sea-ice in 2016. Nat Commun, 2019, 10: 13 CrossRef ADS Google Scholar

[9] Funk S, Gilad E, Watkins C. The spread of awareness and its impact on epidemic outbreaks. Proc Natl Acad Sci USA, 2009, 106: 6872-6877 CrossRef ADS Google Scholar

[10] He M, Miyajima F, Roberts P. Emergence and global spread of epidemic healthcare-associated Clostridium difficile. Nat Genet, 2013, 45: 109-113 CrossRef Google Scholar

[11] Valdano E, Fiorentin M R, Poletto C. Epidemic Threshold in Continuous-Time Evolving Networks. Phys Rev Lett, 2018, 120: 068302 CrossRef ADS arXiv Google Scholar

[12] Angstmann C N, Erickson A M, Henry B I. Fractional Order Compartment Models. SIAM J Appl Math, 2017, 77: 430-446 CrossRef Google Scholar

[13] Galea S, Riddle M, Kaplan G A. Causal thinking and complex system approaches in epidemiology. Int J Epidemiology, 2010, 39: 97-106 CrossRef Google Scholar

[14] Brockmann D, Helbing D. The Hidden Geometry of Complex, Network-Driven Contagion Phenomena. Science, 2013, 342: 1337-1342 CrossRef ADS Google Scholar

[15] Arino J, Ducrot A, Zongo P. A metapopulation model for malaria with transmission-blocking partial immunity in hosts. J Math Biol, 2012, 64: 423-448 CrossRef Google Scholar

[16] Hufnagel L, Brockmann D, Geisel T. Forecast and control of epidemics in a globalized world. Proc Natl Acad Sci USA, 2004, 101: 15124-15129 CrossRef ADS arXiv Google Scholar

[17] Human Mobility Networks, Travel Restrictions, and the Global Spread of 2009 H1N1 Pandemic. PLoS ONE, 2011, 6: e16591 CrossRef ADS Google Scholar

[18] Wesolowski A, Eagle N, Tatem A J. Quantifying the Impact of Human Mobility on Malaria. Science, 2012, 338: 267-270 CrossRef ADS Google Scholar

[19] Gao C, Liu J. Modeling and Restraining Mobile Virus Propagation. IEEE Trans Mobile Comput, 2013, 12: 529-541 CrossRef Google Scholar

[20] Wang X, Ni W, Zheng K. Virus Propagation Modeling and Convergence Analysis in Large-Scale Networks. IEEE TransInformForensic Secur, 2016, 11: 2241-2254 CrossRef Google Scholar

[21] Li Q, Brass A L, Ng A. A genome-wide genetic screen for host factors required for hepatitis C virus propagation. Proc Natl Acad Sci USA, 2009, 106: 16410-16415 CrossRef ADS Google Scholar

[22] Fraser C, Donnelly C A, Cauchemez S. Pandemic Potential of a Strain of Influenza A (H1N1): Early Findings. Science, 2009, 324: 1557-1561 CrossRef ADS Google Scholar

[23] Wang J, Wang X, Wu J. Inferring metapopulation propagation network for intra-city epidemic control and prevention. In: Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery $\&$ Data Mining, 2018. 830--838. Google Scholar

[24] Chen Y C, Li Y J, Tseng A, et al. Deep learning for malicious flow detection. In: Proceedings of 2017 IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC), 2017. 1--7. Google Scholar

[25] Wang W, Liu Q H, Liang J. Coevolution spreading in complex networks. Phys Rep, 2019, 820: 1-51 CrossRef ADS arXiv Google Scholar

[26] Ogura M, Mei W, Sugimoto K. Synergistic Effects in Networked Epidemic Spreading Dynamics. IEEE Trans Circuits Syst II, 2020, 67: 496-500 CrossRef Google Scholar

[27] Chen S, Small M, Fu X. Global Stability of Epidemic Models With Imperfect Vaccination and Quarantine on Scale-Free Networks. IEEE Trans Netw Sci Eng, 2020, 7: 1583-1596 CrossRef Google Scholar

[28] Koher A, Lentz H H K, Gleeson J P. Contact-Based Model for Epidemic Spreading on Temporal Networks. Phys Rev X, 2019, 9: 031017 CrossRef ADS arXiv Google Scholar

[29] Chang L, Duan M, Sun G. Cross-diffusion-induced patterns in an SIR epidemic model on complex networks. Chaos, 2020, 30: 013147 CrossRef ADS Google Scholar

[30] Li M Y, Muldowney J S. Global stability for the SEIR model in epidemiology. Math Biosci, 1995, 125: 155-164 CrossRef Google Scholar

[31] Yang Z, Zeng Z, Wang K. Modified SEIR and AI prediction of the epidemics trend of COVID-19 in China under public health interventions. J Thorac Dis, 2020, 12: 165-174 CrossRef Google Scholar

[32] Hochreiter S, Schmidhuber J. Long Short-Term Memory. Neural Computation, 1997, 9: 1735-1780 CrossRef Google Scholar

[33] Yuan Y. Recent advances in trust region algorithms. Math Program, 2015, 151: 249-281 CrossRef Google Scholar

[34] Du Z, Xu X, Wu Y, et al. The serial interval of COVID-19 from publicly reported confirmed cases. medRxiv, 2020, DOI: https://doi.org/10.1101/2020.02. Google Scholar

  • Figure 1

    (Color online) The structure of LSTM model.

  • Figure 2

    (Color online) The prediction of infected population via LSTM, where $I_{\rm~Pred}^{\rm~(a)}$ and $I_{\rm~Pred}^{\rm~(b)}$ denote the prediction of 10 days and 20 days, respectively.

  • Figure 3

    (Color online) The structure of the sliding window method. Therein, $I_i$ denotes the $i$th window.

  • Figure 4

    (Color online) MAPE with different values of $E$(0) of the test set.

  • Figure 5

    (Color online) Parameter identification with different values of $E(0)$ on different days. (a) $E(0)=8$; protectłinebreak (b) $E(0)=56$; (c) parameters for January 10; (d) parameters for February 16.

  • Figure 6

    (Color online) Prediction of the infected population. On the left part of the dashed straight line, we show the training of the data, whereas on the right part, we give the prediction results of the test data. (a) Prediction of the training set and test set; (b) prediction of the next 100 days from March 17.

  • Figure 7

    (Color online) Prediction of the infected population based on the traditional SEIR model and the modified SEIR model on different training data sets: (a) from January 10 to February 13, (b) from January 10 to February 14, protectłinebreak (c) from January 10 to February 15, and (d) from January 10 to February 16.

  • Figure 8

    (Color online) Prediction of the infected populations in provinces around Hubei.

  • Figure 9

    (Color online) Prediction of the infected populations in provinces in Yangtze River Delta.

  • Table 1  

    Table 1Prediction of the infected population on different training data sets

    Training data set Test data set $\rm~MAPE_1$ (%) $\rm~MAPE_2$ (%)
    01-10–02-13 (35 d) 02-17–03-08 (21 d) 5.5004 5.4720
    01-10–02-14 (36 d) 02-17–03-08 (21 d) 4.2543 2.1176
    01-10–02-15 (37 d) 02-17–03-08 (21 d) 2.0342 2.1118
    01-10–02-16 (38 d) 02-17–03-08 (21 d) 2.3528 2.6669