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Modeling the second outbreak of COVID19 with isolation and contact tracing
1.  Complex Systems Research Center, Shanxi University, Taiyuan 030006, China 
2.  Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis, on Disease Control and Prevention, Shanxi University, Taiyuan 030006, China 
3.  Data Science and Technology, North University of China, Taiyuan 030051, China 
4.  Department of Mathematics, Xinzhou Teachers University, Xinzhou 034000, China 
5.  College of Arts and Sciences, Shanxi Agricultural University, Taigu 030801, China 
6.  School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, China 
7.  Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton T6G 2G1, Canada 
8.  School of Public Health, Peking University, Beijing 100191, China 
9.  Centre for Diseases Modeling (CDM), Laboratory of Mathematical Parallel Systems (LAMPS), Department of Mathematics and Statistics, York University, Toronto M3J 1P3, Canada 
10.  School of Mathematical Sciences, Fudan University, Shanghai 200433, China 
The first case of Corona Virus Disease 2019 (COVID19) was reported in Wuhan, China in December 2019. Since then, COVID19 has quickly spread out to all provinces in China and over 150 countries or territories in the world. With the first level response to public health emergencies (FLRPHE) launched over the country, the outbreak of COVID19 in China is achieving under control in China. We develop a mathematical model based on the epidemiology of COVID19, incorporating the isolation of healthy people, confirmed cases and contact tracing measures. We calculate the basic reproduction numbers 2.5 in China (excluding Hubei province) and 2.9 in Hubei province with the initial time on January 30 which shows the severe infectivity of COVID19, and verify that the current isolation method effectively contains the transmission of COVID19. Under the isolation of healthy people, confirmed cases and contact tracing measures, we find a noteworthy phenomenon that is the second epidemic of COVID19 and estimate the peak time and value and the cumulative number of cases. Simulations show that the contact tracing measures can efficiently contain the transmission of the second epidemic of COVID19. With the isolation of all susceptible people or all infectious people or both, there is no second epidemic of COVID19. Furthermore, resumption of work and study can increase the transmission risk of the second epidemic of COVID19.
References:
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Centers for Disease Control and Prevention, Coronavirus Disease 2019 (COVID19), Available from: https://www.cdc.gov/coronavirus/2019ncov/index.html. Google Scholar 
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Chinese Center for Disease Control and Prevention,, Available from: http://2019ncov.chinacdc.cn/2019nCoV/. Google Scholar 
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[7] 
T. Chen, J. Rui, Q. Wang, et al., A mathematical model for simulating the phasebased transmissibility of a novel coronavirus, Infectious Diseases of Poverty, 9 (2020), 18. Google Scholar 
[8] 
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio R_{0} in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365382. doi: 10.1007/BF00178324. Google Scholar 
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T. Frieden, A strong public health system: Essential for health and economic progress, China CDC Weekly, 2 (2020), 128130. Google Scholar 
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W. Guan, Clinical characteristics of 2019 novel coronavirus infection in China, MedRxiv, 2020. Google Scholar 
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A. B. Gumel, et al., Modelling strategies for controlling SARS outbreaks, Proceedings of the Royal Society of London. Series B: Biological Sciences, 271 (2004), 22232232. Google Scholar 
[15] 
H. Haario, et al., DRAM: efficient adaptive MCMC, Stat. Comput., 16 (2006), 339354. doi: 10.1007/s1122200694380. Google Scholar 
[16] 
W. M. Hirsch, H. Hanisch and J.P. Gabriel, Differential equation models of some parasitic infections: Methods for the study of asymptotic behavior, Comm. Pure Appl. Math., 38 (1985), 733753. doi: 10.1002/cpa.3160380607. Google Scholar 
[17] 
B. Huang, J. Wang, J. Cai, et al., Integrated vaccination and physical distancing interventions to prevent future COVID19 waves in Chinese cities, Nature Human Behaviour, 5 (2021), 695705. Google Scholar 
[18] 
C. Huang, et al., Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China, The Lancet, 395 (2020), 497506. doi: 10.3934/mbe.2020148. Google Scholar 
[19] 
N. Imai, et al, Estimating the potential total number of novel Coronavirus (2019nCoV) cases in Wuhan City, China, Preprint published by the Imperial College London, 2020. Google Scholar 
[20] 
P. R. Krause, T. R. Fleming, I. M. Longini, et al., SARSCoV2 variants and vaccines, New England Journal of Medicine, 385 (2021), 179186. Google Scholar 
[21] 
R. Li, et al., Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARSCoV2), Science, 368 (2020), 489493. Google Scholar 
[22] 
Z. Liu, et al., Predicting the cumulative number of cases for the COVID19 epidemic in China from early data, Math. Biosci. Eng., 17 (2020), 30403051. doi: 10.3934/mbe.2020172. Google Scholar 
[23] 
R. Lu, et al., Genomic characterisation and epidemiology of 2019 novel coronavirus: implications for virus origins and receptor binding, The Lancet, 395 (2020), 565574. Google Scholar 
[24] 
M. S. Majumder, et al., Estimation of MERScoronavirus reproductive number and case fatality rate for the spring 2014 Saudi Arabia outbreak: Insights from publicly available data, PLoS Currents, 6 (2014). Google Scholar 
[25] 
J. Read, et al., Novel coronavirus 2019nCoV: Early estimation of epidemiological parameters and epidemic predictions, MedRxiv, 2020. Google Scholar 
[26] 
M. Shen, Z. Peng, Y. Xiao, et al., Modeling the epidemic trend of the 2019 novel coronavirus outbreak in China, The Innovation, 1 (2020), 100048. Google Scholar 
[27] 
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems: An Introduction to the Theory of Competitive and Cooperative Systems, American Mathematical Soc., 2008. Google Scholar 
[28] 
H. Song, S. Liu and W. Jiang, Global dynamics of a multistage SIR model with distributed delays and nonlinear incidence rate, Math. Methods Appl. Sci., 40 (2017), 21532164. doi: 10.1002/mma.4130. Google Scholar 
[29] 
H. Song, D. Tian and C. Shan, Modeling the effect of temperature on dengue virus transmission with periodic delay differential equations, Math. Biosci. Eng., 17 (2020), 41474164. doi: 10.3934/mbe.2020230. Google Scholar 
[30] 
H. Song, et al., Using travellerderived cases in Henan Province to quantify the spread of COVID19 in Wuhan, China, Nonlinear Dynamics, 101 (2020), 18211831. Google Scholar 
[31] 
H. Song, et al., Estimation of COVID19 outbreak size in Harbin, China, Nonlinear Dynamics, 106 (2021), 12291237. Google Scholar 
[32] 
B. Tang, et al., Estimation of the transmission risk of the 2019nCoV and its implication for public health interventions, Journal of Clinical Medicine, 9 (2020), 462. Google Scholar 
[33] 
H. Tian, Y. Liu, Y. Li, et al., An investigation of transmission control measures during the first 50 days of the COVID19 epidemic in China, Science, 368 (2020), 638642. Google Scholar 
[34] 
J. Tian, J. Wu, Y. Bao, et al., Modeling analysis of COVID19 based on morbidity data in Anhui, China, Math. Biosci. Eng., 17 (2020), 28422852. doi: 10.3934/mbe.2020158. Google Scholar 
[35] 
W. Tu, et al., Epidemic update and risk assessment of 2019 novel coronavirusChina, January 28, 2020, China CDC Weekly, 2 (2020), 8386. doi: 10.3934/mbe.2020148. Google Scholar 
[36] 
P. van den Driessche and J. Watmough, Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 2948. doi: 10.1016/S00255564(02)001086. Google Scholar 
[37] 
K. Wang, Z. Lu, X. Wang, et al., Current trends and future prediction of novel coronavirus disease (COVID19) epidemic in China: A dynamical modeling analysis, Math. Biosci. Eng., 17 (2020), 30523061. doi: 10.3934/mbe.2020173. Google Scholar 
[38] 
J. Wu, et al., Quantifying the role of social distancing, personal protection and case detection in mitigating COVID19 outbreak in Ontario, Canada, J. Math. Ind., 10 (2020), Paper No. 15, 12 pp. doi: 10.1186/s13362020000833. Google Scholar 
[39] 
Y. Yang, et al., Epidemiological and clinical features of the 2019 novel coronavirus outbreak in China, MedRxiv, 2020. Google Scholar 
[40] 
S. You, H. Wang, M. Zhang, et al., Assessment of monthly economic losses in Wuhan under the lockdown against COVID19, Humanities and Social Sciences Communications, 7 (2020), 112. Google Scholar 
[41] 
S. Zhao, et al., Preliminary estimation of the basic reproduction number of novel coronavirus (2019nCoV) in China, from 2019 to 2020: A datadriven analysis in the early phase of the outbreak, International Journal of Infectious Diseases, 92 (2020), 214217. Google Scholar 
[42] 
N. Zhu, A novel coronavirus from patients with pneumonia in China, 2019, New England Journal of Medicine, 382 (2020), 727733. Google Scholar 
show all references
References:
[1] 
Centers for Disease Control and Prevention, Coronavirus Disease 2019 (COVID19), Available from: https://www.cdc.gov/coronavirus/2019ncov/index.html. Google Scholar 
[2] 
Chinese Center for Disease Control and Prevention,, Available from: http://2019ncov.chinacdc.cn/2019nCoV/. Google Scholar 
[3] 
National Health Commission of the People's Republic of China,, Available from: http://en.nhc.gov.cn/. Google Scholar 
[4] 
World Health Organization (WHO), Coronavirus Disease (COVID19) Pandemic, Available from: https://www.who.int/emergencies/diseases/novelcoronavirus2019. Google Scholar 
[5] 
World Health Organization (WHO), Coronavirus Disease (COVID2019) Situation Reports, Available from: https://www.who.int/emergencies/diseases/novelcoronavirus2019/situationreports/. Google Scholar 
[6] 
World Health Organization (WHO), Coronavirus Disease (COVID2019) Outbreak, Report of the WHOChina Joint Mission on COVID19, Available from: https://www.who.int/docs/defaultsource/coronaviruse/whochinajointmissiononcovid19finalreport.pdf. Google Scholar 
[7] 
T. Chen, J. Rui, Q. Wang, et al., A mathematical model for simulating the phasebased transmissibility of a novel coronavirus, Infectious Diseases of Poverty, 9 (2020), 18. Google Scholar 
[8] 
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio R_{0} in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365382. doi: 10.1007/BF00178324. Google Scholar 
[9] 
M. Egger, et al., Developing WHO guidelines: Time to formally include evidence from mathematical modelling studies, F1000Research, 6 (2017). Google Scholar 
[10] 
M. Elisabeth, Covid19: UK starts social distancing after new model points to 260000 potential deaths, BMJ, 368 (2020), m1089. Google Scholar 
[11] 
T. Frieden, A strong public health system: Essential for health and economic progress, China CDC Weekly, 2 (2020), 128130. Google Scholar 
[12] 
M. Gilbert, et al., Preparedness and vulnerability of African countries against importations of COVID19: A modelling study, The Lancet, 395 (2020), 871877. Google Scholar 
[13] 
W. Guan, Clinical characteristics of 2019 novel coronavirus infection in China, MedRxiv, 2020. Google Scholar 
[14] 
A. B. Gumel, et al., Modelling strategies for controlling SARS outbreaks, Proceedings of the Royal Society of London. Series B: Biological Sciences, 271 (2004), 22232232. Google Scholar 
[15] 
H. Haario, et al., DRAM: efficient adaptive MCMC, Stat. Comput., 16 (2006), 339354. doi: 10.1007/s1122200694380. Google Scholar 
[16] 
W. M. Hirsch, H. Hanisch and J.P. Gabriel, Differential equation models of some parasitic infections: Methods for the study of asymptotic behavior, Comm. Pure Appl. Math., 38 (1985), 733753. doi: 10.1002/cpa.3160380607. Google Scholar 
[17] 
B. Huang, J. Wang, J. Cai, et al., Integrated vaccination and physical distancing interventions to prevent future COVID19 waves in Chinese cities, Nature Human Behaviour, 5 (2021), 695705. Google Scholar 
[18] 
C. Huang, et al., Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China, The Lancet, 395 (2020), 497506. doi: 10.3934/mbe.2020148. Google Scholar 
[19] 
N. Imai, et al, Estimating the potential total number of novel Coronavirus (2019nCoV) cases in Wuhan City, China, Preprint published by the Imperial College London, 2020. Google Scholar 
[20] 
P. R. Krause, T. R. Fleming, I. M. Longini, et al., SARSCoV2 variants and vaccines, New England Journal of Medicine, 385 (2021), 179186. Google Scholar 
[21] 
R. Li, et al., Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARSCoV2), Science, 368 (2020), 489493. Google Scholar 
[22] 
Z. Liu, et al., Predicting the cumulative number of cases for the COVID19 epidemic in China from early data, Math. Biosci. Eng., 17 (2020), 30403051. doi: 10.3934/mbe.2020172. Google Scholar 
[23] 
R. Lu, et al., Genomic characterisation and epidemiology of 2019 novel coronavirus: implications for virus origins and receptor binding, The Lancet, 395 (2020), 565574. Google Scholar 
[24] 
M. S. Majumder, et al., Estimation of MERScoronavirus reproductive number and case fatality rate for the spring 2014 Saudi Arabia outbreak: Insights from publicly available data, PLoS Currents, 6 (2014). Google Scholar 
[25] 
J. Read, et al., Novel coronavirus 2019nCoV: Early estimation of epidemiological parameters and epidemic predictions, MedRxiv, 2020. Google Scholar 
[26] 
M. Shen, Z. Peng, Y. Xiao, et al., Modeling the epidemic trend of the 2019 novel coronavirus outbreak in China, The Innovation, 1 (2020), 100048. Google Scholar 
[27] 
H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems: An Introduction to the Theory of Competitive and Cooperative Systems, American Mathematical Soc., 2008. Google Scholar 
[28] 
H. Song, S. Liu and W. Jiang, Global dynamics of a multistage SIR model with distributed delays and nonlinear incidence rate, Math. Methods Appl. Sci., 40 (2017), 21532164. doi: 10.1002/mma.4130. Google Scholar 
[29] 
H. Song, D. Tian and C. Shan, Modeling the effect of temperature on dengue virus transmission with periodic delay differential equations, Math. Biosci. Eng., 17 (2020), 41474164. doi: 10.3934/mbe.2020230. Google Scholar 
[30] 
H. Song, et al., Using travellerderived cases in Henan Province to quantify the spread of COVID19 in Wuhan, China, Nonlinear Dynamics, 101 (2020), 18211831. Google Scholar 
[31] 
H. Song, et al., Estimation of COVID19 outbreak size in Harbin, China, Nonlinear Dynamics, 106 (2021), 12291237. Google Scholar 
[32] 
B. Tang, et al., Estimation of the transmission risk of the 2019nCoV and its implication for public health interventions, Journal of Clinical Medicine, 9 (2020), 462. Google Scholar 
[33] 
H. Tian, Y. Liu, Y. Li, et al., An investigation of transmission control measures during the first 50 days of the COVID19 epidemic in China, Science, 368 (2020), 638642. Google Scholar 
[34] 
J. Tian, J. Wu, Y. Bao, et al., Modeling analysis of COVID19 based on morbidity data in Anhui, China, Math. Biosci. Eng., 17 (2020), 28422852. doi: 10.3934/mbe.2020158. Google Scholar 
[35] 
W. Tu, et al., Epidemic update and risk assessment of 2019 novel coronavirusChina, January 28, 2020, China CDC Weekly, 2 (2020), 8386. doi: 10.3934/mbe.2020148. Google Scholar 
[36] 
P. van den Driessche and J. Watmough, Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 2948. doi: 10.1016/S00255564(02)001086. Google Scholar 
[37] 
K. Wang, Z. Lu, X. Wang, et al., Current trends and future prediction of novel coronavirus disease (COVID19) epidemic in China: A dynamical modeling analysis, Math. Biosci. Eng., 17 (2020), 30523061. doi: 10.3934/mbe.2020173. Google Scholar 
[38] 
J. Wu, et al., Quantifying the role of social distancing, personal protection and case detection in mitigating COVID19 outbreak in Ontario, Canada, J. Math. Ind., 10 (2020), Paper No. 15, 12 pp. doi: 10.1186/s13362020000833. Google Scholar 
[39] 
Y. Yang, et al., Epidemiological and clinical features of the 2019 novel coronavirus outbreak in China, MedRxiv, 2020. Google Scholar 
[40] 
S. You, H. Wang, M. Zhang, et al., Assessment of monthly economic losses in Wuhan under the lockdown against COVID19, Humanities and Social Sciences Communications, 7 (2020), 112. Google Scholar 
[41] 
S. Zhao, et al., Preliminary estimation of the basic reproduction number of novel coronavirus (2019nCoV) in China, from 2019 to 2020: A datadriven analysis in the early phase of the outbreak, International Journal of Infectious Diseases, 92 (2020), 214217. Google Scholar 
[42] 
N. Zhu, A novel coronavirus from patients with pneumonia in China, 2019, New England Journal of Medicine, 382 (2020), 727733. Google Scholar 
Related parameters and initial values in (China excluding Hubei province)  
Parameter  Descriptions  Mean value  95% CI  Source 
α_{1}  The time of isolation at home for susceptible people  1/14  –  [3] 
β  The transmission rate of COVID19  0.3567  (0.3291, 0.3815)  Estimated 
b  The average number of contact tracing  12  (11.5448, 12.5346)  Estimated 
γ  The hospitalization rate of infectious people  0.1429  (0.1306, 0.1538)  Estimated 
δ  The discharged rate from hospital  0.0949  –  Calculated 
μ  The transfer rate from susceptible to isolated susceptible people  1.76 × 10^{−4}  (1.66 × 10^{−4}, 1.86 × 10^{−4})  Estimated 
α_{2}  The transfer rate from isolated susceptible to susceptible people  5.05 × 10^{−6}  (4.95 × 10^{−6}, 5.15 × 10^{−6})  Estimated 
Initial Values  Descriptions  Mean value  95% CI  Source 
N  Total population of China (excluding Hubei province)  1.3362 × 10^{9}  –  [3] 
S_{1}(0)  The number of initial susceptible people  2.6723 × 10^{8}  (2.6723 × 10^{8}, 2.6723 × 10^{8})  Estimated 
S_{2}(0)  The number of initial quarantined susceptible people  3762  (3754, 3772)  Estimated 
S_{3}(0)  The number of initial isolated susceptible people  1.069 × 10^{9}  (1.069 × 10^{9}, 1.069 × 10^{9})  Estimated 
I_{1}(0)  The number of initial unfound infectious people  4101  (4091, 4115)  Estimated 
I_{2}(0)  The number of initial quarantined infectious people  700  (695,706)  Estimated 
H(0)  The number of initial hospitalized people  3886  –  Data 
R(0)  The number of initial removed people  64  –  Data 
Related parameters and initial values (in Hubei province)  
Parameter  Descriptions  Mean value  95% CI  Source 
α_{1}  The time of isolation at home for susceptible people  1/14  –  [3] 
β  The transmission rate of COVID19  0.3999  (0.3845, 0.4045)  Estimated 
b  The average number of contact tracing  5  (4.968, 5.1203)  Estimated 
γ  The hospitalization rate of infectious people  0.1379  (0.1289, 0.1490)  Estimated 
δ  The discharged rate from hospital  1/18  –  Calculated 
μ  The transfer rate from susceptible to isolated susceptible people  9.983 × 10^{−6}  (9.56 × 10^{−6}, 1.02 × 10^{5})  Estimated 
α_{2}  The transfer rate from isolated susceptible to susceptible people  4.825 × 10^{5}  (4.7606 × 10^{5}, 4.9615 × 10^{5})  Estimated 
Initial Values  Descriptions  Mean value  95% CI  Source 
N  Total population of Hubei province  5.917 × 10^{7}  –  [3] 
S_{1}(0)  The number of initial susceptible people  1.18 × 10^{7}  (1.18 × 10^{7}, 1.18 × 10^{7})  Estimated 
S_{2}(0)  The number of initial quarantined susceptible people  5367  (5352, 5382)  Estimated 
S_{3}(0)  The number of initial isolated susceptible people  4.7336 × 10^{7}  (4.7336 × 10^{7}, 4.7336 × 10^{7})  Estimated 
I_{1}(0)  The number of initial unfound infectious people  12973  (12963, 12985)  Estimated 
I_{2}(0)  The number of initial quarantined infectious people  2023  (2014, 2029)  Estimated 
H(0)  The number of initial hospitalized people  5806  –  Data 
R(0)  The number of initial removed people  320  –  Data 
Notes: 95% CI: 95% highest posterior density interval. 
Related parameters and initial values in (China excluding Hubei province)  
Parameter  Descriptions  Mean value  95% CI  Source 
α_{1}  The time of isolation at home for susceptible people  1/14  –  [3] 
β  The transmission rate of COVID19  0.3567  (0.3291, 0.3815)  Estimated 
b  The average number of contact tracing  12  (11.5448, 12.5346)  Estimated 
γ  The hospitalization rate of infectious people  0.1429  (0.1306, 0.1538)  Estimated 
δ  The discharged rate from hospital  0.0949  –  Calculated 
μ  The transfer rate from susceptible to isolated susceptible people  1.76 × 10^{−4}  (1.66 × 10^{−4}, 1.86 × 10^{−4})  Estimated 
α_{2}  The transfer rate from isolated susceptible to susceptible people  5.05 × 10^{−6}  (4.95 × 10^{−6}, 5.15 × 10^{−6})  Estimated 
Initial Values  Descriptions  Mean value  95% CI  Source 
N  Total population of China (excluding Hubei province)  1.3362 × 10^{9}  –  [3] 
S_{1}(0)  The number of initial susceptible people  2.6723 × 10^{8}  (2.6723 × 10^{8}, 2.6723 × 10^{8})  Estimated 
S_{2}(0)  The number of initial quarantined susceptible people  3762  (3754, 3772)  Estimated 
S_{3}(0)  The number of initial isolated susceptible people  1.069 × 10^{9}  (1.069 × 10^{9}, 1.069 × 10^{9})  Estimated 
I_{1}(0)  The number of initial unfound infectious people  4101  (4091, 4115)  Estimated 
I_{2}(0)  The number of initial quarantined infectious people  700  (695,706)  Estimated 
H(0)  The number of initial hospitalized people  3886  –  Data 
R(0)  The number of initial removed people  64  –  Data 
Related parameters and initial values (in Hubei province)  
Parameter  Descriptions  Mean value  95% CI  Source 
α_{1}  The time of isolation at home for susceptible people  1/14  –  [3] 
β  The transmission rate of COVID19  0.3999  (0.3845, 0.4045)  Estimated 
b  The average number of contact tracing  5  (4.968, 5.1203)  Estimated 
γ  The hospitalization rate of infectious people  0.1379  (0.1289, 0.1490)  Estimated 
δ  The discharged rate from hospital  1/18  –  Calculated 
μ  The transfer rate from susceptible to isolated susceptible people  9.983 × 10^{−6}  (9.56 × 10^{−6}, 1.02 × 10^{5})  Estimated 
α_{2}  The transfer rate from isolated susceptible to susceptible people  4.825 × 10^{5}  (4.7606 × 10^{5}, 4.9615 × 10^{5})  Estimated 
Initial Values  Descriptions  Mean value  95% CI  Source 
N  Total population of Hubei province  5.917 × 10^{7}  –  [3] 
S_{1}(0)  The number of initial susceptible people  1.18 × 10^{7}  (1.18 × 10^{7}, 1.18 × 10^{7})  Estimated 
S_{2}(0)  The number of initial quarantined susceptible people  5367  (5352, 5382)  Estimated 
S_{3}(0)  The number of initial isolated susceptible people  4.7336 × 10^{7}  (4.7336 × 10^{7}, 4.7336 × 10^{7})  Estimated 
I_{1}(0)  The number of initial unfound infectious people  12973  (12963, 12985)  Estimated 
I_{2}(0)  The number of initial quarantined infectious people  2023  (2014, 2029)  Estimated 
H(0)  The number of initial hospitalized people  5806  –  Data 
R(0)  The number of initial removed people  320  –  Data 
Notes: 95% CI: 95% highest posterior density interval. 
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