Epidemiological Model for COVID-19 in China
PDF

Keywords

Basic reproduction number
Coronavirus disease 2019
Epidemic forecast
Epidemiology
Mathematical model

DOI

10.36922/itps.v3i2.938

Abstract

Background. The epidemic of coronavirus disease 2019 (COVID-19) caused by the SARS-CoV-2 first broke out in Wuhan, Hubei Province in China, and then spread quickly worldwide.

Objective. This study aimed to dissect the spread and end of the epidemic in China with a precise mathematical model.

Methods. Various data were obtained from the official websites of the Chinese National Health from January 20 to July 8, 2020. The Chinese study participants were divided into three groups, namely, Hubei (including Wuhan), nationwide without Hubei, and Henan. The basic reproduction number (R0), effective reproduction number (Rt), and gender and age ratio of COVID-19 were calculated, and the epidemic’s predicted curves or fitting curves with peak time and end time were plotted with SIR model. These predicted curves were compared with actual scatter plots.

Results. The fitting curve of the Hubei group showed a parabola with a peak on February 18, 2020, with 51,673 cases and the gradual decrease of infected patients, which culminates with a downhill after May 2020. During early outbreak, the highest recorded R0 was 6.13, which declined gradually forming a S-type curve, and it approached zero in early May. Similar to Hubei group, the fitting curve of the nationwide without Hubei group also showed a parabola, recording a peak of 9145 cases on February 10, 2020. At first, its R0 was as high as 2.35 but declined to zero in early April. The epidemic in the Henan group also reached its peak on February 10, 2020, and ended in early April as well.

Conclusion. The epidemic development of COVID-19 in China followed the shape of parabolic curves. This model provides insights into how to strategize for epidemic control.

References

Huang, C.; Wang, Y.; Li, X.; Ren, L.; Zhao, J.; Hu, Y.; Zhang, L.; Fan, G.; Xu, J.; Gu, X.; Cheng, Z.; Yu, T.; Xia, J.; Wei, Y.; Wu, W.; Xie, X.; Yin, W.; Li, H.; Liu, M.; Xiao, Y.; Gao, H.; Guo, L.; Xie, J.; Wang, G.; Jiang, R.; Gao, Z.; Jin, Q.; Wang, J.; Cao, B. Clinical Features of Patients Infected with 2019 Novel Coronavirus in Wuhan, China. Lancet, 2020, 395(10223), 497–506.

Bulut, C.; Kato, Y. Epidemiology of COVID-19. Turk. J. Med. Sci., 2020, 50(SI-1), 563–570.

Chen, N.; Zhou, M.; Dong, X.; Qu, J.; Gong, F.; Han, Y.; Qiu, Y.; Wang, J.; Liu, Y.; Wei, Y.; Xia, J.A.; Yu, T.; Zhang, X.; Zhang, L. Epidemiological and Clinical Characteristics of 99 Cases of 2019 Novel Coronavirus Pneumonia in Wuhan, China: A Descriptive Study. Lancet, 2020, 395(10223), 507–513.

Eurosurveillance Editorial Team. Note from the Editors: World Health Organization Declares Novel Coronavirus (2019-nCoV) Sixth Public Health Emergency of International Concern. Euro. Surveill., 2020, 25(5), 200131e.

Du, Z.; Wang, L.; Cauchemez, S.; Xu, X.; Wang, X.; Cowling, B.J.; Meyers, L.A., Risk for Transportation of Coronavirus Disease from Wuhan to Other Cities in China. Emerg. Infect. Dis., 2020, 26(5), 1049–1052.

World Health Organization. Coronavirus Disease (COVID-2019) Situation Reports. Geneva: World Health Organization; 2020. Available from: https://www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports. [Last accessed on 2020 Jul 16].

Nishiura, H.; Jung, S.M.; Linton, N.M.; Kinoshita, R.; Yang, Y.; Hayashi, K.; Kobayashi, T.; Yuan, B.; Akhmetzhanov, A.R. The Extent of Transmission of Novel Coronavirus in Wuhan, China, 2020. J. Clin. Med., 2020, 9(2), 330.

Anastassopoulou, C.; Russo, L.; Tsakris, A.; Siettos, C. Data-based Analysis, Modelling and Forecasting of the COVID-19 Outbreak. PLoS One, 2020, 15(3), e0230405.

Osthus, D.; Hickmann, K.S.; Caragea, P.C.; Higdon, D.; Del Valle, S.Y. Forecasting Seasonal Influenza with a State-space SIR Model. Ann. Appl. Stat., 2017, 11(1), 202–224.

Mukhtar, A.Y.A.; Munyakazi, J.B.; Ouifki, R.; Clark, A.E. Modelling the Effect of Bednet Coverage on Malaria Transmission in South Sudan. PLoS One, 2018, 13(6), e0198280.

Buceta, J.; Johnson, K. Modeling the Ebola Zoonotic Dynamics: Interplay between Enviroclimatic Factors and Bat Ecology. PLoS One, 2017, 12(6), e0179559.

Althouse, B.M.; Lessler, J.; Sall, A.A.; Diallo, M.; Hanley, K.A.; Watts, D.M.; Weaver, S.C.; Cummings, D.A.T. Synchrony of Sylvatic Dengue Isolations: A Multi-host, Multi-vector SIR Model of Dengue Virus Transmission in Senegal. PLoS Negl. Trop. Dis., 2012, 6(11), e1928.

Zhang, Z. The Outbreak Pattern of SARS Cases in China as Revealed by a Mathematical Model. Ecol. Modell., 2007, 204(3), 420–426.

Cooper, I.; Mondal, A.; Antonopoulos, C.G. A SIR Model Assumption for the Spread of COVID-19 in Different Communities. Chaos Solitons Fractals, 2020, 139, 110057.

Neves, A.G.M.; Guerrero, G. Predicting the Evolution of the COVID-19 Epidemic with the A-SIR Model: Lombardy, Italy and São Paulo state, Brazil. Physica D, 2020, 413, 132693.

Gezer, N.S.; Ergan, B.; Bar??, M.M.; Appak, Ö.; Say?ner, A.A.; Balc?, P.; Kuruüzüm, Z.; Çavu?, S.A.; K?l?nç, O. COVID-19 S: A New Proposal for Diagnosis and Structured Reporting of COVID-19 on Computed Tomography Imaging. Diagn. Interv. Radiol., 2020, 26(4), 315–322.

Jin, Y.H.; Cai, L.; Cheng, Z.S.; Cheng, H.; Deng, T.; Fan, Y.P.; Fang, C.; Huang, D.; Huang, L.Q.; Huang, Q.; Han, Y.; Hu, B.; Hu, F.; Li, B.H.; Li, Y.R.; Liang, K.; Lin, L.K.; Luo, L.S.; Ma, J.; Ma, L.L.; Peng, Z.Y.; Pan, Y.B.; Pan, Z.Y.; Ren, X.Q.; Sun, H.M.; Wang, Y.; Wang, Y.Y.; Weng, H.; Wei, C.J.; Wu, D.F.; Xia, J.; Xiong, Y.; Xu, H.B.; Yao, X.M.; Yuan, Y.F.; Ye, T.S.; Zhang, X.C.; Zhang, Y.W.; Zhang, Y.G.; Zhang, H.M.; Zhao, Y.; Zhao, M.J.; Zi, H.; Zeng, X.T.; Wang, Y.Y.; Wang, X.H.; for the Zhongnan Hospital of Wuhan University Novel Coronavirus Management and Research Team, Evidence-Based Medicine Chapter of China International Exchange and Promotive Association for Medical and Health Care (CPAM). A Rapid Advice Guideline for the Diagnosis and Treatment of 2019 Novel Coronavirus (2019-nCoV) Infected Pneumonia (Standard Version). Mil. Med. Res., 2020, 7(1), 4.

National Bureau of Statistic. National Census; 2015. Available from: http://www.stats.gov.cn/tjsj/zxfb/201604/t20160420_1346151. html. [Last accessed on 2020 Jul 16].

Breban, R.; Vardavas, R.; Blower, S. Theory Versus Data: How to Calculate R0? PLoS One, 2007, 2(3), e282.

Pellis, L.; Ferguson, N.M.; Fraser, C. Threshold Parameters for a Model of Epidemic Spread among Households and Workplaces. J. R. Soc. Interface, 2009, 6(40), 979–987.

Wu, J.T.; Leung, K.; Leung, G.M. Nowcasting and Forecasting the Potential Domestic and International Spread of the 2019- nCoV Outbreak Originating in Wuhan, China: A Modelling Study. Lancet, 2020, 395(10225), 689–697.

Ridenhour, B.; Kowalik, J.M.; Shay, D.K. Unraveling R0: Considerations for Public Health Applications. Am. J. Public Health, 2014, 104(2), e32–e41.

Zhao, S.; Lin, Q.; Ran, J.; Musa, S.S.; Yang, G.; Wang, W.; Lou, Y.; Gao, D.; Yang, L.; He, D.; Wang, M.H. 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., 2020, 92, 214–217.

Li, Q.; Guan, X.; Wu, P.; Wang, X.; Zhou, L.; Tong, Y.; Ren, R.; Leung, K.S.M.; Lau, E.H.Y.; Wong, J.Y.; 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, T.T.Y.; Wu, J.T.; Gao, G.F.; Cowling, B.J.; Yang, B.; Leung, G.M.; Feng, Z. Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus-infected Pneumonia. N. Engl. J. Med., 2020, 382(13), 1199–1207.

Riou, J.; Althaus, C.L. Pattern of Early Human-to-human Transmission of Wuhan 2019 Novel Coronavirus (2019-nCoV), December 2019 to January 2020. Euro. Surveill., 2020, 25(4), 2000058.

Sanche, S.; Lin, Y.T.; Xu, C.; Romero-Severson, E.; Hengartner, N.; Ke, R. High Contagiousness and Rapid Spread of Severe Acute Respiratory Syndrome Coronavirus 2. Emerg. Infect. Dis., 2020, 26(7), 1470–1477.

Zhao, S.; Musa, S.S.; Lin, Q.; Ran, J.; Yang, G.; Wang, W.; Lou, Y.; Yang, L.; Gao, D.; He, D.; Wang, M.H. Estimating the Unreported Number of Novel Coronavirus (2019-nCoV) Cases in China in the First Half of January 2020: A Data-driven Modelling Analysis of the Early Outbreak. J. Clin. Med., 2020, 9(2), 388.

Steven Riley, S.; Fraser, C.; Donnelly, C.A.; Ghani, A.C.; Abu- Raddad, L.J.; Hedley, A.J.; Leung, G.M.; Ho, L.M.; Lam, T.H.; Thach, T.Q.; Chau, P.; Chan, K.P.; Lo, S.V.; Leung, P.Y.; Tsang, T.; Ho, W.; Lee, K.H.; Lau, E.M.C.; Ferguson, N.M.; Anderson, R.M. Transmission Dynamics of the Etiological agent of SARS in Hong Kong: Impact of Public Health Interventions. Science, 2003, 300(5627), 1961–1966.

Wallinga, J.; Teunis, P. Different Epidemic Curves for Severe Acute Respiratory Syndrome Reveal Similar Impacts of Control Measures. Am. J. Epidemiol., 2004, 160(6), 509–516.

Majumder, M.S.; Rivers, C.; Lofgren, E.; Fisman, D. Estimation of MERS-coronavirus Reproductive Number and Case Fatality Rate for the Spring 2014 Saudi Arabia Outbreak: Insights from Publicly Available Data. PLoS Curr., 2014, 6, cd5f5fe133c.

Kim, S.; Choi, S.; Ko, Y.; Ki, M.; Jung, E. Risk Estimation of the SARS-CoV-2 Acute Respiratory Disease Outbreak Outside China. Theor. Biol. Med. Model, 2020, 17(1), 9.

Zhou, P.; Yang, X.L.; Wang, X.G.; Hu, B.; Zhang, L.; Zhang, W.; Si, H.R.; Zhu, Y.; Li, B.; Huang, C.L.; Chen, H.D.; Chen, J.; Luo, Y.; Guo, H.; Jiang, R.D.; Liu, M.Q.; Chen, Y.; Shen, X.R.; Wang, X.; Zheng, X.S.; Zhao, K.; Chen, Q.J.; Deng, F.; Liu, L.L.; Yan, B.; Zhan, F.X.; Wang, Y.Y.; Xiao, G.F.; Shi, Z.L. A Pneumonia Outbreak Associated with a New Coronavirus of Probable Bat Origin. Nature, 2020, 579(7798), 270–273.

Lu, R.; Zhao, X.; Li, J.; Niu, P.; Yang, B.; Wu, H.; Wang, W.; Song, H.; Huang, B.; Zhu, N.; Bi, Y.; Ma, X.; Zhan, F.; Wang, L.; Hu, T.; Zhou, H.; Hu, Z.; Zhou, W.; Zhao, L.; Chen, J.; Meng, Y.; Wang, J.; Lin, Y.; Yuan, J.; Xie, Z.; Ma, J.; Liu, W.J.; Wang, D.; Xu, W.; Holmes, E.C.; Gao, G.F.; Wu, G.; Chen, W.; Shi, W.; Tan, W. Genomic Characterisation and Epidemiology of 2019 Novel Coronavirus: Implications for Virus Origins and Receptor Binding. Lancet, 2020, 395(10224), 565–574.

Wilder-Smith, A.; Freedman, D.O. Isolation, Quarantine, Social Distancing and Community Containment: Pivotal Role for Old-style Public Health Measures in the Novel Coronavirus (2019- nCoV) Outbreak. J. Travel Med., 2020, 27(2), taaa020.

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.