Search Advanced

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 6: 7502-7518. doi: 10.3934/mbe.2020383
Previous Article Next Article
Research article Special Issues

Predicting COVID-19 using past pandemics as a guide: how reliable were mathematical models then, and how reliable will they be now?

  • 1.
    Department of Mathematics, The University of Ottawa, 150 Louis-Pasteur Pvt, Ottawa, ON K1N 6N5, Canada
  • 2.
    Department of Mathematics & Statistics and School of Biological Sciences, Washington State University, PO Box 643113, Pullman, WA, 99164-3113, USA
  • 3.
    Department of Mathematics and Faculty of Medicine, The University of Ottawa, 150 Louis-Pasteur Pvt, Ottawa, ON K1N 6N5, Canada
  • Received: 31 August 2020 Accepted: 23 October 2020 Published: 30 October 2020

  • During the earliest stages of a pandemic, mathematical models are a tool that can be imple-mented quickly. However, such models are based on meagre data and limited biological understanding. We evaluate the accuracy of various models from recent pandemics (SARS, MERS and the 2009 H1N1 outbreak) as a guide to whether we can trust the early model predictions for COVID-19. We show that early models can have good predictive power for a disease's first wave, but they are less predictive of the possibility of a second wave or its strength. The models with the highest accuracy tended to include stochasticity, and models developed for a particular geographic region are often applicable in other regions. It follows that mathematical models developed early in a pandemic can be useful for long-term predictions, at least during the first wave, and they should include stochastic variations, to represent unknown characteristics inherent in the earliest stages of all pandemics.

    Citation: Christian Costris-Vas, Elissa J. Schwartz, Robert Smith?. Predicting COVID-19 using past pandemics as a guide: how reliable were mathematical models then, and how reliable will they be now?[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 7502-7518. doi: 10.3934/mbe.2020383

    Related Papers:

  • During the earliest stages of a pandemic, mathematical models are a tool that can be imple-mented quickly. However, such models are based on meagre data and limited biological understanding. We evaluate the accuracy of various models from recent pandemics (SARS, MERS and the 2009 H1N1 outbreak) as a guide to whether we can trust the early model predictions for COVID-19. We show that early models can have good predictive power for a disease's first wave, but they are less predictive of the possibility of a second wave or its strength. The models with the highest accuracy tended to include stochasticity, and models developed for a particular geographic region are often applicable in other regions. It follows that mathematical models developed early in a pandemic can be useful for long-term predictions, at least during the first wave, and they should include stochastic variations, to represent unknown characteristics inherent in the earliest stages of all pandemics.


    加载中


    [1] Y. Liu, A. A. Gayle, A. Wilder-Smith, J. Rocklöv, The Reproductive Number of COVID-19 Is Higher Compared to SARS Coronavirus, J. Travel Med.e 27 (2020), taaa021. doi: 10.1093/jtm/taaa021
    [2] Q. Li. X. Guan, P. Wu, X. Wang, L. Zhou, Y. Tong, et al., Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus-Infected Pneumonia, N. Engl. J. Med., 382 (2020), 1199-1207. doi: 10.1056/NEJMoa2001316
    [3] W. Wang, J. Tang, F. Wei, Updated understanding of the outbreak of 2019 novel coronavirus (2019nCoV) in Wuhan, China, J. Med. Virol. 92 (2020), 441-447. doi: 10.1002/jmv.25689
    [4] K. Kousha, M. Thelwall, COVID-19 publications: Database coverage, citations, readers, tweets, news, Facebook walls, Reddit posts, Quant. Sci. Stud. 1 (2020), 1068-1091. doi: 10.1162/qss_a_00066
    [5] J. M. Heffernan, R. J. Smith, L. M. Wahl, Perspectives on the basic reproductive ratio, J. R. Soc. Interface 2 (2005), 281-293. doi: 10.1098/rsif.2005.0042
    [6] J. Li, D. Blakeley, R. J. Smith?, The Failure of R0, Comp. Math. Methods Med., 2011 (2011), 527610.
    [7] B. Tang, X. Wang, Q. Li, N. L. Bragazzi, S. Tang, Y. Xiao, et al., Estimation of the Transmission Risk of the 2019-NCoV and Its Implication for Public Health Interventions, J. Clin. Med., 9 (2020), 462. doi: 10.3390/jcm9020462
    [8] N. Imai, A. Cori, I. Dorigatti, M. Baguelin, C. Donnelly, S. Riley, et al., Report 3: Transmissibility of 2019-nCoV, Imperial College London (2020) 1-6.
    [9] S. Zhao, Q. Lin, J. Ran, S. S. Musa, G. Yang, W. Wang, et al., Preliminary estimation of the basic reproduction number of novel coronavirus (2019-nCoV) in China, from 2019 to 2020: A data-driven analysis in the early phase of the outbreak, Int. J. Infect. Dis., 92 (2020), 214-217. doi: 10.1016/j.ijid.2020.01.050
    [10] J. T. Wu, K. Leung, G.M. Leung, Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study, Lancet, 395 (2020), 689-697. doi: 10.1016/S0140-6736(20)30260-9
    [11] J. Riou, C. L. Althaus, Pattern of early human-to-human transmission of Wuhan 2019-nCoV, Euro. Surveil., 25 (2020), pii = 2000058.
    [12] R. D. Smith, Responding to Global Infectious Disease Outbreaks: Lessons from SARS on the Role of Risk Perception, Communication and Management. Soc. Sci. Med., 63 (2006), 3113-3123. doi: 10.1016/j.socscimed.2006.08.004
    [13] World Health Organization, Summary of Probable SARS Cases with Onset of Illness from 1 November 2002 to 31 July 2003, https://www.who.int/csr/sars/country/table2004_04_21/en/. Accessed 13 Oct 2020.
    [14] S. Riley, C. Fraser, C. A. Donnelly, A. C. Ghani, L. J. Abu-Raddad, A. J. Hedley, et al., Transmission Dynamics of the Etiological Agent of SARS in Hong Kong: Impact of Public Health Interventions, Science, 300 (2003), 1961-1966. doi: 10.1126/science.1086478
    [15] G. Chowell, P. W. Fenimore, M. A. Castillo-Garsow, C. C. Castillo-Chavez, SARS Outbreaks in Ontario, Hong Kong and Singapore: The Role of Diagnosis and Isolation as a Control Mechanism, J. Theor. Biol., 224 (2003), 1-8. doi: 10.1016/S0022-5193(03)00228-5
    [16] M. Lipsitch, T. Cohen, B. Cooper, J. M. Robins, S. Ma, L. James, et al., Transmission Dynamics and Control of Severe Acute Respiratory Syndrome, Science, 300 (2003), 1966-1970. doi: 10.1126/science.1086616
    [17] G. Zhou, G. Yan. Severe Acute Respiratory Syndrome Epidemic in Asia, Emerging Infect. Dis., 9 (2003), 1608-1610.
    [18] B. C. K. Choi, A. W. P. Pak. A Simple Approximate Mathematical Model to Predict the Number of Severe Acute Respiratory Syndrome Cases and Deaths, J. Epidemiology Community Health, 57 (2003), 831-835. doi: 10.1136/jech.57.10.831
    [19] L. O. Lloyd-Smith, A. P. Galvani, W. M. Getz, Curtailing Transmission of Severe Acute Respiratory Syndrome within a Community and Its Hospital, Proc. Royal Soc. B, 270, (2003), 1979-1989. doi: 10.1098/rspb.2003.2481
    [20] S. A. Eifan, I. Nour, A. Hanif, A. M. Zamzam, S. M. AlJohani, A Pandemic Risk Assessment of Middle East Respiratory Syndrome Coronavirus (MERS-CoV) in Saudi Arabia, Saudi J. Biol. Sci., 24 (2017), 1631-1638. doi: 10.1016/j.sjbs.2017.06.001
    [21] G. Chowell, F. Abdirizak, S. Lee, J. Lee, E. Jung, H. Nishiura, et al., Transmission Characteristics of MERS and SARS in the Healthcare Setting: A Comparative Study, BMC Med., 13 (2015), 210. doi: 10.1186/s12916-015-0450-0
    [22] C. Drosten, B. Meyer, M. A. Müller, V. M. Corman, M. Al-Masri, R. Hossain, et al., Transmission of MERS-coronavirus in household contacts, N. Engl. J. Med., 371 (2014), 828-835. doi: 10.1056/NEJMoa1405858
    [23] S. Cauchemez, C. Fraser, M. D. Van Kerkhove, C. A. Donnelly, S. Riley, A. Rambaut, et al., Middle East Respiratory Syndrome Coronavirus: Quantification of the Extent of the Epidemic, Surveillance Biases, and Transmissibility, Lancet Infect. Dis., 14 (2014), 50-56. doi: 10.1016/S1473-3099(13)70304-9
    [24] R. Breban, J. Riou, A. Fontanet, Interhuman Transmissibility of Middle East Respiratory Syndrome Coronavirus: Estimation of Pandemic Risk, Lancet, 382 (2013), 694-699. doi: 10.1016/S0140-6736(13)61492-0
    [25] H.-J. Chang, Estimation of Basic Reproduction Number of the Middle East Respiratory Syndrome Coronavirus (MERS-CoV) during the Outbreak in South Korea, 2015, BioMed. Eng. OnLine, 16 (2017), 79. doi: 10.1186/s12938-017-0370-7
    [26] Centers for Disease Control, H1N1 Flu Pandemic Timeline. Centers for Disease Control and Prevention, https://www.cdc.gov/flu/pandemic-resources/2009-pandemic-timeline.html, Accessed 13 Oct 2020.
    [27] T. N. Jilani, R. T. Jamil, A. H. Siddiqui, H1N1 Influenza (Swine Flu). StatPearls, 2020, http://www.ncbi.nlm.nih.gov/books/NBK513241/ Accessed 13 Oct 2020.
    [28] Centers for Disease Control, 2009 H1N1 Pandemic (H1N1pdm09 virus), https://www.cdc.gov/flu/pandemic-resources/2009-h1n1-pandemic.html Accessed 13 Oct 2020.
    [29] M. G. Roberts, H. Nishiura, Early Estimation of the Reproduction Number in the Presence of Imported Cases: Pandemic Influenza H1N1-2009 in New Zealand, PLoS ONE, 6 (2011), e17835. doi: 10.1371/journal.pone.0017835
    [30] C. Fraser, C. A. Donnelly, S. Cauchemez, W. P. Hanage, M. D. Van Kerkhove, T. D. Hollingsworth, et al., Pandemic Potential of a Strain of Influenza A (H1N1): Early Findings, Science, 324 (2009), 1557-1561. doi: 10.1126/science.1176062
    [31] H. Nishiura, C. Castillo-Chavez, M. Safan M, G. Chowell, Transmission Potential of the New Influenza A(H1N1) Virus and Its Age-Specificity in Japan, Euro. Surveil., 14 (2009), 19227.
    [32] L. F. White, J. Wallinga, L. Finelli, C. Reed, S. Riley, M. Lipsitch, et al., Estimation of the Reproductive Number and the Serial Interval in Early Phase of the 2009 Influenza A/H1N1 Pandemic in the USA, Influenza Other Respir. Viruses, 3 (2009), 267-276. doi: 10.1111/j.1750-2659.2009.00106.x
    [33] L. C. Mostąo-Guidolin, C. S. Bowman, A. L. Greer, D. N. Fisman, S. M. Moghadas, Transmissibility of the 2009 H1N1 Pandemic in Remote and Isolated Canadian Communities: A Modelling Study, BMJ Open, 2 (2012), e001614. doi: 10.1136/bmjopen-2012-001614
    [34] M. Helferty, J. Vachon, J. Tarasuk, R. Rodin, J. Spika, L. Pelletier, Incidence of Hospital Admissions and Severe Outcomes during the First and Second Waves of Pandemic (H1N1) 2009, CMAJ, 182 (2010), 1981-1987. doi: 10.1503/cmaj.100746
    [35] O. T. Mytton, P. D. Rutter, M. Mak, E. A. Stanton, N. Sachedina, L. J. Donaldson, Mortality Due to Pandemic (H1N1) 2009 Influenza in England: A Comparison of the First and Second Waves, Epidemiol. Infect., 140 (2012), 1533-1541. doi: 10.1017/S0950268811001968
    [36] I. Dorigatti, S. Cauchemez, N. M. Ferguson, Increased Transmissibility Explains the Third Wave of Infection by the 2009 H1N1 Pandemic Virus in England, Proc. Natl. Acad. Sci. U.S.A., 110 (2013), 13422-13427. doi: 10.1073/pnas.1303117110
    [37] O. Sharomi, C. N. Podder, A. B. Gumel, S. M. Mahmud, E. Rubinstein, Modelling the Transmission Dynamics and Control of the Novel 2009 Swine Influenza (H1N1) Pandemic, Bull. Math. Biol., 73 (2011), 515-548. doi: 10.1007/s11538-010-9538-z
    [38] M. A. Jhung, D. Swerdlow, S. J. Olsen, D. Jernigan, M. Biggerstaff, L. Kamimoto, et al., Epidemiology of 2009 pandemic influenza A (H1N1) in the United States, Clin. Infect. Dis., 52 (2011), S13-S26. doi: 10.1093/cid/ciq008
    [39] M. D. Van Kerkhove, A. W. Mounts, S. Mall, K. A. Vandemaele, M. Chamberland, T. dos Santos, et al., Epidemiologic and virologic assessment of the 2009 influenza A (H1N1) pandemic on selected temperate countries in the Southern Hemisphere: Argentina, Australia, Chile, New Zealand and South Africa, Influenza Other Respir. Viruses, 5 (2011), e487-e498. doi: 10.1111/j.1750-2659.2011.00249.x
    [40] R. J. Smith?, Did we Eradicate SARS? Lessons Learned and the Way Forward, Am. J. Biomed. Sci. Res., 6 (2019), 001017.
    [41] R. M. Anderson, C. Fraser, A. C. Ghani, C. A. Donnelly, S. Riley, N. M. Ferguson, et al., Epidemiology, Transmission Dynamics and Control of SARS: The 2002-2003 Epidemic, Philos. Trans. R. Soc. Lond., B, Biol. Sci., 359 (2004), 1091-105. doi: 10.1098/rstb.2004.1490
    [42] S. Ruan, W. Wang, S. A. Levin, The Effect of Global Travel on the Spread of SARS, Math. Biosci. Eng., 3 (2006), 205-218. doi: 10.3934/mbe.2006.3.205
    [43] N. G. Becker, K. Glass, Z. Li, G. K. Aldis, Controlling Emerging Infectious Diseases like SARS, Math. Biosci., 193 (2005), 205-121. doi: 10.1016/j.mbs.2004.07.006
    [44] A. J. Kucharski, C. L. Althaus, The role of superspreading in Middle East respiratory syndrome coronavirus (MERS-CoV) transmission, Euro. Surveil. 20 (2015), 14-18.
    [45] S. Bernard-Stoecklin, B. Nikolay, A. Assiri, A. A. Saeed, P. K. Embarek, H. El Bushra, et al., Comparative Analysis of Eleven Healthcare-Associated Outbreaks of Middle East Respiratory Syndrome Coronavirus (Mers-Cov) from 2015 to 2017, Sci. Rep., 9 (2019), 1-9. doi: 10.1038/s41598-018-37186-2
    [46] S. Choi, E. Jung, B. Y. Choi, Y. J. Hur, M. Ki, High Reproduction Number of Middle East Respiratory Syndrome Coronavirus in Nosocomial Outbreaks: Mathematical Modelling in Saudi Arabia and South Korea, J. Hosp. Infect., 99 (2018), 162-168. doi: 10.1016/j.jhin.2017.09.017
    [47] T. Sardar, I. Ghosh, X. Rodó, J. Chattopadhyay, A Realistic Two-Strain Model for MERS-CoV Infection Uncovers the High Risk for Epidemic Propagation, PLOS Negl. Trop. Dis., 14 (2020), e0008065. doi: 10.1371/journal.pntd.0008065
    [48] M. S. Majumder, C. Rivers, E. Lofgren, D. Fisman. Estimation of MERS-Coronavirus Reproductive Number and Case Fatality Rate for the Spring 2014 Saudi Arabia Outbreak: Insights from Publicly Available Data, PLoS Currents, 6 (2014).
    [49] P. Poletti, M. Ajelli, S. Merler, The effect of risk perception on the 2009 H1N1 pandemic influenza dynamics, PLoS One, 6 (2011), e16460. doi: 10.1371/journal.pone.0016460
    [50] S. Tsukui, Case-Based Surveillance of Pandemic (H1N1) 2009 in Maebashi City, Japan, Jpn. J. Infect. Dis., 65 (2012), 132-137.
    [51] G. Chowell, S. Echevarria-Zuno, C. Viboud, L. Simonsen, J. Tamerius, M. A. Miller, et al., Characterizing the epidemiology of the 2009 influenza A/H1N1 pandemic in Mexico, PLoS Med., 8 (2011), e1000436. doi: 10.1371/journal.pmed.1000436
    [52] C. M. Rivers, E. T. Lofgren, M. Marathe, S. Eubank, B. L. Lewis, Modeling the impact of interventions on an epidemic of Ebola in Sierra Leone and Liberia, PLOS Currents Outbreaks, 6 (2014).
    [53] D. Fisman, E. Khoo, A. Tuite, Early epidemic dynamics of the West African 2014 Ebola outbreak: Estimates derived with a simple two-parameter model, PLoS Currents, 6 (2014).
    [54] C. Browne, H. Gulbudak, G. Webb, Modeling contact tracing in outbreaks with application to Ebola, J. Theor. Biol., 384 (2015), 33-49. doi: 10.1016/j.jtbi.2015.08.004
    [55] G. Webb, C. Browne, A model of the Ebola epidemics in West Africa incorporating age of infection, J. Biol. Dyn., 10 (2016), 18-30. doi: 10.1080/17513758.2015.1090632
    [56] T. S. Do, Y. S. Lee, Modeling the spread of Ebola. Osong Public Health and Research Perspectives, 7 (2016), 43-48. doi: 10.1016/j.phrp.2015.12.012
    [57] D. Salem, R. Smith?, A Mathematical Model of Ebola Virus Disease: Using Sensitivity Analysis to Determine Effective Intervention Targets, Proceedings of the SummerSim-SCSC 2016 conference, (2016), 16-23.
    [58] P. Bhandari, Analysis of Prediction Models in spread of Ebola Virus Disease, Thesis, Deakin University (2019).
    [59] T. C. Germann, K. Kadau, I. M. Longini, C. A. Macken, Mitigation strategies for pandemic influenza in the United States, Proc. Natl. Acad. Sci.U. S.A., 103 (2006), 5935-5940. doi: 10.1073/pnas.0601266103
    [60] J. T. Wu, B. J. Cowling, The use of mathematical models to inform influenza pandemic preparedness and response, Exp. Biol. Med., 236 (2011), 955-961. doi: 10.1258/ebm.2010.010271
    [61] S. S. Morse, J. A. Mazet, M. Woolhouse, C. R. Parrish, D. Carroll, W. B. Karesh, et al., Prediction and prevention of the next pandemic zoonosis, Lancet, 380 (2012), 1956-1965. doi: 10.1016/S0140-6736(12)61684-5
    [62] A. Huppert, G. Katriel, Mathematical modelling and prediction in infectious disease epidemiology, Clin. Microbiol. Infect., 19 (2013), 999-1005. doi: 10.1111/1469-0691.12308
    [63] P. Saunders-Hastings, B. Q. Hayes, R. Smith? D. Krewski. Modelling community-control strategies to protect hospital resources during an influenza pandemic in Ottawa, Canada, PloS One, 12 (2017), e0179315. doi: 10.1371/journal.pone.0174953
    [64] M. Valenciano, E. Kissling, J. M. Cohen, N. Oroszi, A. S. Barret, C. Rizzo, et al., Estimates of pandemic influenza vaccine effectiveness in Europe, 2009-2010: results of Influenza Monitoring Vaccine Effectiveness in Europe (I-MOVE) multicentre case-control study, PLoS Med., 8 (2011), e1000388. doi: 10.1371/journal.pmed.1000388
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
3.9

Metrics

Article views(14421) PDF downloads(190) Cited by(0)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Figures(4)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog