Skip to main content
PMC home page
Springer Nature - PMC COVID-19 Collection logoLink to Springer Nature - PMC COVID-19 Collection
. 2020 May 28;14(5):613–622. doi: 10.1007/s11684-020-0787-4

Estimation of reproduction numbers of COVID-19 in typical countries and epidemic trends under different prevention and control scenarios

Chen Xu 1,#, Yinqiao Dong 2,#, Xiaoyue Yu 1,#, Huwen Wang 1,#, Lhakpa Tsamlag 1,#, Shuxian Zhang 1,#, Ruijie Chang 1,#, Zezhou Wang 3,5,#, Yuelin Yu 1,#, Rusi Long 1,#, Ying Wang 1, Gang Xu 1, Tian Shen 1, Suping Wang 1, Xinxin Zhang 4,✉, Hui Wang 1,✉, Yong Cai 1,✉
PMCID: PMC7255828  PMID: 32468343

Abstract

The coronavirus disease 2019 (COVID-19) has become a life-threatening pandemic. The epidemic trends in different countries vary considerably due to different policy-making and resources mobilization. We calculated basic reproduction number (R0) and the time-varying estimate of the effective reproductive number (Rt) of COVID-19 by using the maximum likelihood method and the sequential Bayesian method, respectively. European and North American countries possessed higher R0 and unsteady Rt fluctuations, whereas some heavily affected Asian countries showed relatively low R0 and declining Rt now. The numbers of patients in Africa and Latin America are still low, but the potential risk of huge outbreaks cannot be ignored. Three scenarios were then simulated, generating distinct outcomes by using SEIR (susceptible, exposed, infectious, and removed) model. First, evidence-based prompt responses yield lower transmission rate followed by decreasing Rt. Second, implementation of effective control policies at a relatively late stage, in spite of huge casualties at early phase, can still achieve containment and mitigation. Third, wisely taking advantage of the time-window for developing countries in Africa and Latin America to adopt adequate measures can save more people’s life. Our mathematical modeling provides evidence for international communities to develop sound design of containment and mitigation policies for COVID-19.

Electronic Supplementary Material

Supplementary material is available in the online version of this article at 10.1007/s11684-020-0787-4 and is accessible for authorized users.

Keywords: reproduction number, SEIR model, COVID-19, estimate

Supplementary information

11684_2020_787_MOESM1_ESM.pdf (312.8KB, pdf)

Sensitivity analysis on serial interval distribution

Acknowledgements

This work is funded by Medicine and Engineering Interdisciplinary Research Fund of Shanghai Jiao Tong University (No. YG2020YQ06), the National Key Research and Development Project (Nos. 2018YFC1705100, 2018YFC1705103, and 2018YFC2000700) and the National Natural Science Foundation of China (Nos. 71673187 and 81630086), the Key Research Program (No. ZDRW-ZS-2017-1) of the Chinese Academy of Sciences, Innovative research team of high-level local universities in Shanghai. We acknowledge all healthcare workers involved in the diagnosis, treatment, and prevention of COVID-19 all around world. We thank WHO and other institutes for coordinating data collection for patients with COVID-19.

Compliance with ethics guideline

Chen Xu, Yinqiao Dong, Xiaoyue Yu, Huwen Wang, Lhakpa Tsamlag, Shuxian Zhang, Ruijie Chang, Zezhou Wang, Yuelin Yu, Rusi Long, Ying Wang, Gang Xu, Tian Shen, Suping Wang, Xinxin Zhang, HuiWang, and Yong Cai declare no competing interests. The data sets analyzed for this study can be found in the reports of the World Health Organization (WHO) (https://www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports/). This manuscript does not involve a research protocol requiring approval by the relevant institutional review board or ethics committee.

Footnotes

These authors contributed equally to this manuscript.

Contributor Information

Xinxin Zhang, Email: zhangx@shsmu.edu.cn.

Hui Wang, Email: huiwang@shsmu.edu.cn.

Yong Cai, Email: caiyong202028@hotmail.com.

References

  • 1.WHO. Coronavirus disease 2019 (COVID-19) Situation Report—68. 2020. [Google Scholar]
  • 2.WHO. WHO Director-General’s opening remarks at the media briefing on COVID-19—11 March 2020. 2020. [Google Scholar]
  • 3.WHO. Coronavirus disease 2019 (COVID-19) Situation Report—54. 2020. [Google Scholar]
  • 4.Choi JY. Postgrad Med J. 2020. COVID-19 in South Korea. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 5.Ministry of Health, Singapore. Tighter measures to minimise further spread of COVID-19. 2020. [Google Scholar]
  • 6.Li LF. Novel coronavirus pneumonia: Japan’s internal worries and countermeasures. 2020. [Google Scholar]
  • 7.Zhang S, Wang Z, Chang R, Wang H, Xu C, Yu X, Tsamlag L, Dong Y, Wang H, Cai Y. COVID-19 containment: China provides important lessons for global response. Front Med. 2020;14(2):215–219. doi: 10.1007/s11684-020-0766-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 8.Cori A, Boëlle PY, Thomas G, Leung GM, Valleron AJ. Temporal variability and social heterogeneity in disease transmission: the case of SARS in Hong Kong. PLOS Comput Biol. 2009;5(8):e1000471. doi: 10.1371/journal.pcbi.1000471. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 9.Fukutome A, Watashi K, Kawakami N, Ishikawa H. Mathematical modeling of severe acute respiratory syndrome nosocomial transmission in Japan: the dynamics of incident cases and prevalent cases. Microbiol Immunol. 2007;51(9):823–832. doi: 10.1111/j.1348-0421.2007.tb03978.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 10.Fang H, Chen J, Hu J. Modelling the SARS epidemic by a latticebased Monte-Carlo simulation. Conf Proc IEEE Eng Med Biol Soc. 2005;2005:7470–7473. doi: 10.1109/IEMBS.2005.1616239. [DOI] [PubMed] [Google Scholar]
  • 11.Read JM, Bridgen JR, Cummings DA, Ho A, Jewell CP. medRxiv. 2020. Novel coronavirus 2019-nCoV: early estimation of epidemiological parameters and epidemic predictions. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 12.Ai L. medRxiv. 2020. Modelling the epidemic trend of the 2019-nCOV outbreak in Hubei Province, China. [Google Scholar]
  • 13.Chang R, Wang H, Zhang S, Wang Z, Dong Y, Tsamlag L, Yu X, Xu C, Yu Y, Long R, Liu N, Chu Q, Wang Y, Xu G, Shen T, Wang S, Deng X, Huang J, Zhang X, Wang H, Cai Y. Phase- and epidemic region-adjusted estimation of the number of coronavirus disease 2019 cases in China. Front Med. 2020;14(2):199–209. doi: 10.1007/s11684-020-0768-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 14.Wang H, Wang Z, Dong Y, Chang R, Xu C, Yu X, Zhang S, Tsamlag L, Shang M, Huang J, Wang Y, Xu G, Shen T, Zhang X, Cai Y. Phase-adjusted estimation of the number of coronavirus disease 2019 cases in Wuhan, China. Cell Discov. 2020;6(1):10. doi: 10.1038/s41421-020-0148-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 15.National Health Commission of the People’s Republic of China. Outbreak notification. 2020. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 16.Imai N, et al. Report 3: Transmissibility of 2019-nCoV. March 11. 2020. [Google Scholar]
  • 17.Li Q, Guan X, Wu P, Wang X, Zhou L, Tong Y, Ren R, Leung KSM, Lau EHY, Wong JY, Xing X, Xiang N, Wu Y, Li C, Chen Q, Li D, Liu T, Zhao J, Liu M, Tu W, Chen C, Jin L, Yang R, Wang Q, Zhou S, Wang R, Liu H, Luo Y, Liu Y, Shao G, Li H, Tao Z, Yang Y, Deng Z, Liu B, Ma Z, Zhang Y, Shi G, Lam TTY, Wu JT, Gao GF, Cowling BJ, Yang B, Leung GM, Feng Z. Early transmission dynamics in Wuhan, China, of novel coronavirus-infected pneumonia. N Engl J Med. 2020;382(13):1199–1207. doi: 10.1056/NEJMoa2001316. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 18.Tang B, Wang X, Li Q, Bragazzi NL, Tang S, Xiao Y, Wu J. Estimation of the transmission risk of the 2019-nCoV and its implication for public health interventions. J Clin Med. 2020;9(2):E462. doi: 10.3390/jcm9020462. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 19.Ni H. Will the new epidemic “global pandemic” be out of control if countries do not adopt the Chinese model? 2020. [Google Scholar]
  • 20.WHO. Coronavirus disease (COVID-2019) situation reports. 2020. [Google Scholar]
  • 21.Obadia T, Haneef R, Boëlle PY. The R0 package: a toolbox to estimate reproduction numbers for epidemic outbreaks. BMC Med Inform Decis Mak. 2012;12(1):147. doi: 10.1186/1472-6947-12-147. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 22.Nikbakht R, Baneshi MR, Bahrampour A. Estimation of the basic reproduction number and vaccination coverage of influenza in the United States (2017–18) J Res Health Sci. 2018;18(4):e00427. [PMC free article] [PubMed] [Google Scholar]
  • 23.White LF, Wallinga J, Finelli L, Reed C, Riley S, Lipsitch M, Pagano M. 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. 2009;3(6):267–276. doi: 10.1111/j.1750-2659.2009.00106.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 24.Cori A, Ferguson NM, Fraser C, Cauchemez S. A new framework and software to estimate time-varying reproduction numbers during epidemics. Am J Epidemiol. 2013;178(9):1505–1512. doi: 10.1093/aje/kwt133. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 25.WHO Ebola Response Team. Aylward B, Barboza P, Bawo L, Bertherat E, Bilivogui P, Blake I, Brennan R, Briand S, Chakauya JM, Chitala K, Conteh RM, Cori A, Croisier A, Dangou JM, Diallo B, Donnelly CA, Dye C, Eckmanns T, Ferguson NM, Formenty P, Fuhrer C, Fukuda K, Garske T, Gasasira A, Gbanyan S, Graaff P, Heleze E, Jambai A, Jombart T, Kasolo F, Kadiobo AM, Keita S, Kertesz D, Koné M, Lane C, Markoff J, Massaquoi M, Mills H, Mulba JM, Musa E, Myhre J, Nasidi A, Nilles E, Nouvellet P, Nshimirimana D, Nuttall I, Nyenswah T, Olu O, Pendergast S, Perea W, Polonsky J, Riley S, Ronveaux O, Sakoba K S G, Krishnan R, Senga M, Shuaib F, Van Kerkhove MD, Vaz R, Wijekoon Kannangarage N, Yoti Z. Ebola virus disease in West Africa—the first 9 months of the epidemic and forward projections. N Engl J Med. 2014;371(16):1481–1495. doi: 10.1056/NEJMoa1411100. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 26.Kandel N, Chungong S, Omaar A, Xing J. Health security capacities in the context of COVID-19 outbreak: an analysis of International Health Regulations annual report data from 182 countries. Lancet. 2020;395(10229):1047–1053. doi: 10.1016/S0140-6736(20)30553-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 27.Nishiura H, Linton NM, Akhmetzhanov AR. Serial interval of novel coronavirus (COVID-19) infections. Int J Infect Dis. 2020;93:284–286. doi: 10.1016/j.ijid.2020.02.060. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 28.World Bank. Population, total. 2019. [Google Scholar]
  • 29.Desai AN, Kraemer MUG, Bhatia S, Cori A, Nouvellet P, Herringer M, Cohn EL, Carrion M, Brownstein JS, Madoff LC, Lassmann B. Real-time epidemic forecasting: challenges and opportunities. Health Secur. 2019;17(4):268–275. doi: 10.1089/hs.2019.0022. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 30.Polonsky JA, Baidjoe A, Kamvar ZN, Cori A, Durski K, Edmunds WJ, Eggo RM, Funk S, Kaiser L, Keating P d O, Marks M, Moraga P, Morgan O, Nouvellet P, Ratnayake R, Roberts CH, Whitworth J, Jombart T. Outbreak analytics: a developing data science for informing the response to emerging pathogens. Philos Trans R Soc Lond B Biol Sci. 2019;374(1776):20180276. doi: 10.1098/rstb.2018.0276. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 31.The Lancet. COVID-19: learning from experience. Lancet. 2020;395(10229):1011. doi: 10.1016/S0140-6736(20)30686-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 32.Zhang W, Du RH, Li B, Zheng XS, Yang XL, Hu B, Wang YY, Xiao GF, Yan B, Shi ZL, Zhou P. Molecular and serological investigation of 2019-nCoV infected patients: implication of multiple shedding routes. Emerg Microbes Infect. 2020;9(1):386–389. doi: 10.1080/22221751.2020.1729071. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 33.The Lancet. COVID-19: too little, too late? Lancet. 2020;395(10226):755. doi: 10.1016/S0140-6736(20)30522-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 34.Li Z, Wu M, Yao JW, Guo J, Liao X, Song SJ, Li JL, Duan GJ, Zhou YX, Wu XJ, Zhou ZS, Wang TJ, Hu M, Chen XX, Fu Y, Lei C, Dong HL, Xu CO, Hu YH, Han M, Zhou Y, Jia HB, Chen XW, Yan JA. medRxiv. 2020. Caution on kidney dysfunctions of COVID-19 patients. [Google Scholar]
  • 35.Zhou G, Chen S, Chen Z. Back to the spring of 2020: facts and hope of COVID-19 outbreak. Front Med. 2020;14(2):113–116. doi: 10.1007/s11684-020-0758-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 36.Li H, Zhou Y, Zhang M, Wang H, Zhao Q, Liu J. Antimicrob Agents Chemother. 2020. Updated approaches against SARS-CoV-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 37.Li G, De Clercq E. Therapeutic options for the 2019 novel coronavirus (2019-nCoV) Nat Rev Drug Discov. 2020;19(3):149–150. doi: 10.1038/d41573-020-00016-0. [DOI] [PubMed] [Google Scholar]
  • 38.Chen C, Zhang XR, Ju ZY, He WF. Advances in the research of cytokine storm mechanism induced by coronavirus disease 2019 and the corresponding immunotherapies. Chin J Burns (Zhonghua Shao Shang Za Zhi) 2020;36(0):E005. doi: 10.3760/cma.j.cn501120-20200224-00088. [DOI] [PubMed] [Google Scholar]
  • 39.Sina News. The Indonesian President Joko Widodo has appealed to religious leaders to help fight the disease, refusing to close the city but ordering widespread testing. 2020. [Google Scholar]
  • 40.Wang JB. India has introduced 15 measures to prevent the spread of COVID-19. 2020. [Google Scholar]
  • 41.WHO. Do your part to stop stigma and combat COVID-19. 2020. [Google Scholar]
  • 42.Getz WM, Salter R, Mgbara W. Adequacy of SEIR models when epidemics have spatial structure: Ebola in Sierra Leone. Philos Trans R Soc Lond B Biol Sci. 2019;374(1775):20180282. doi: 10.1098/rstb.2018.0282. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 43.Bukhari Q, Jameel Y. SSRN. 2020. Will coronavirus pandemic diminish by summer? [Google Scholar]

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

11684_2020_787_MOESM1_ESM.pdf (312.8KB, pdf)

Sensitivity analysis on serial interval distribution

Articles from Frontiers of Medicine are provided here courtesy of Nature Publishing Group

RESOURCES