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A mathematical model for the novel coronavirus epidemic in Wuhan, China

  • Received: 15 February 2020 Accepted: 09 March 2020 Published: 11 March 2020
  • We propose a mathematical model to investigate the current outbreak of the coronavirus disease 2019 (COVID-19) in Wuhan, China. Our model describes the multiple transmission pathways in the infection dynamics, and emphasizes the role of the environmental reservoir in the transmission and spread of this disease. Our model also employs non-constant transmission rates which change with the epidemiological status and environmental conditions and which reflect the impact of the on-going disease control measures. We conduct a detailed analysis of this model, and demonstrate its application using publicly reported data. Among other findings, our analytical and numerical results indicate that the coronavirus infection would remain endemic, which necessitates long-term disease prevention and intervention programs.

    Citation: Chayu Yang, Jin Wang. A mathematical model for the novel coronavirus epidemic in Wuhan, China[J]. Mathematical Biosciences and Engineering, 2020, 17(3): 2708-2724. doi: 10.3934/mbe.2020148

    Related Papers:

  • We propose a mathematical model to investigate the current outbreak of the coronavirus disease 2019 (COVID-19) in Wuhan, China. Our model describes the multiple transmission pathways in the infection dynamics, and emphasizes the role of the environmental reservoir in the transmission and spread of this disease. Our model also employs non-constant transmission rates which change with the epidemiological status and environmental conditions and which reflect the impact of the on-going disease control measures. We conduct a detailed analysis of this model, and demonstrate its application using publicly reported data. Among other findings, our analytical and numerical results indicate that the coronavirus infection would remain endemic, which necessitates long-term disease prevention and intervention programs.


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    [1] WHO statement regarding cluster of pneumonia cases in Wuhan, China. 2020. Available from: https://www.who.int/china/news/detail/09-01-2020-\who-statement-regarding-cluster-of-pneumonia-cases-in-wuhan-china.
    [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., 2020.
    [3] P. Zhou, X. L. Yang, X. G. Wang, B. Hu, L. Zhang, W. Zhang, et al., Discovery of a novel coronavirus associated with the recent pneumonia outbreak in humans and its potential bat origin, bioRxiv, 2020.
    [4] L. E. Gralinski, V. D. Menachery, Return of the coronavirus: 2019-nCoV, Viruses, 12 (2020), 135.
    [5] T. Ellerin, The new coronavirus: What we do- and don't- know, Harvard Health Blog, January 25, 2020. Available from: https://www.health.harvard.edu/blog/the-new-coronavirus-what-we-do-and-dont-know-2020012518747.
    [6] Centers for Disease Control and Prevention: 2019 novel coronavirus. Available from: https://www.cdc.gov/coronavirus/2019-ncov.
    [7] WHO novel coronavirus (2019-nCoV) situation reports. Available from: https://www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports.
    [8] V. J. Munster, M. Koopmans, N. V. Doremalen, D. V. Riel, E. D. Wit, A novel coronavirus emerging in China - key questions for impact assessment, N. Engl. J. Med., 382 (2020), 692-694.
    [9] WHO statement regarding the outbreak of novel coronavirus (2019-nCoV), 2020. Available from: https://www.who.int/news-room/detail/30-01-2020-statement-on-the-\second-meeting-of-the-international-health-regulations-(2005)-emergency-\committee-regarding-the-outbreak-of-novel-coronavirus-\(2019-ncov).
    [10] C. Rothe, M. Schunk, P. Sothmann, G. Bretzel, G. Froeschl, C. Wallrauch, et al., Transmission of 2019-nCoV Infection from an asymptomatic contact in Germany, N. Engl. J. Med., 2020.
    [11] 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.
    [12] J. M. Read, J. R. E. Bridgen, D. A. T. Cummings, A. Ho, C. P. Jewell, Novel coronavirus 2019-nCoV: early estimation of epidemiological parameters and epidemic predictions, medRxiv, 2020.
    [13] B. Tang, X. Wang, Q. Li, N. L. Bragazzi, S. Tang, Y. Xiao, et al., Estimation of the transmission risk of 2019-nCoV and its implication for public health interventions, J. Clin. Med., 9 (2020), 462.
    [14] N. Imai, A. Cori, I. Dorigatti, M. Baguelin, C. A. Donnelly, S. Riley, et al., Report 3: Transmissi-bility of 2019-nCoV, Reference Source, 2020. Available from: https://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/news--wuhan-coronavirus/.
    [15] H. Zhu, Q. Gao, M. Li, C. Wang, Z. Feng, P. Wang, et al., Host and infectivity prediction of Wuhan 2019 novel coronavirus using deep learning algorithm, bioRxiv, 2020.
    [16] J. F.-W. Chan, S. Yuan, K.-H. Kok, K. K. W. To, H. Chu, J. Yang, et al., A familial cluster of pneumonia associated with the 2019 novel coronavirus indicating person-to-person transmission: a study of a family cluster, Lancet, 395 (2020), 514-523.
    [17] Z. J. Cheng, J. Shan, 2019 Novel coronavirus: where we are and what we know, Infection, (2020), 1-9.
    [18] A. Sahin, A. Erdogan, P. M. Agaoglu, Y. Dineri, A. Cakirci, M. Senel, et al., 2019 novel coronavirus (COVID-19) outbreak: A review of the current literature, Eurasian J. Med. Oncol., 4 (2020), 1-7.
    [19] C. Geller, M. Varbanov, R. E. Duval, Human coronaviruses: Insights into environmental resistance and its influence on the development of new antiseptic strategies, Viruses, 4 (2012), 3044-3068.
    [20] G. Kampf, D. Todt, S. Pfaender, E. Steinmann, Persistence of coronaviruses on inanimate surfaces and its inactivation with biocidal agents, J. Hosp. Infect., 104 (2020), 246-251.
    [21] P. V. D. Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.
    [22] J. P. LaSalle, The Stability of Dynamical Systems, Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1976.
    [23] H. R. Thieme, Persistence under relaxed point-dissipativity (with application to an endemic model), SIAM J. Math. Anal., 24 (1993), 407-435.
    [24] D. Gao, S. Ruan, An SIS patch model with variable transmission coefficients, Math. Biosci., 232 (2011), 110-115.
    [25] M. Y. Li, J. S. Muldowney, P. V. D. Driessche, Global stability of SEIRS models in epidemiology, Can. Appl. Math. Q., 7 (1999), 409-425.
    [26] Z. Shuai, P. V. D. Driessche, Global stability of infectious disease models using Lyapunov functions, SIAM J. Appl. Math., 73 (2013), 1513-1532.
    [27] Wikipedia on the timeline of the 2019-20 Wuhan coronavirus outbreak. Available from https://en.wikipedia.org/wiki/Timeline_of_the_2019\OT1\textendash20_Wuhan_coronavirus_outbreak.
    [28] National Health Commission of China daily reports on novel coronavirus (in Chinese). Available from: http://www.nhc.gov.cn/yjb/pzhgli/new_list.shtml.
    [29] Sina news real-time reports on novel coronavirus (in Chinese). Available from: https://news.sina.cn/zt_d/yiqing0121.
    [30] The government of Wuhan homepage. Available from: http://english.wh.gov.cn/.
    [31] J. A. Spencer, D. P. Shutt, S. K. Moser, H. Clegg, H. J. Wearing, H. Mukundan, et al., Epidemiological parameter review and comparative dynamics of influenza, respiratory syncytial virus, rhinovirus, human coronvirus, and adenovirus, medRxiv, 2020.
    [32] C. Yang, J. Wang, A cholera transmission model incorporating the impact of medical resources, Math. Biosci. Eng., 16 (2019), 5226-5246.
    [33] The Health Commission of Hubei Province. Available from: http://wjw.hubei.gov.cn/fbjd/dtyw/index_16.shtml.
    [34] J. H. Tien, D. J. D. Earn, Multiple transmission pathways and disease dynamics in a waterborne pathogen model, Bull. Math. Biol., 72 (2010), 1506-1533.
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