A Time-Dependent SIR Model for COVID-19 With Undetectable Infected Persons
In this paper, we conduct mathematical and numerical analyses for COVID-19. To predict the trend of COVID-19, we propose a time-dependent SIR model that tracks the transmission and recovering rate at time t. Using the data provided by China authority, we show our one-day prediction errors are almost...
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| Published in | IEEE transactions on network science and engineering Vol. 7; no. 4; pp. 3279 - 3294 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
United States
IEEE
01.10.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
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| Abstract | In this paper, we conduct mathematical and numerical analyses for COVID-19. To predict the trend of COVID-19, we propose a time-dependent SIR model that tracks the transmission and recovering rate at time t. Using the data provided by China authority, we show our one-day prediction errors are almost less than 3%. The turning point and the total number of confirmed cases in China are predicted under our model. To analyze the impact of the undetectable infections on the spread of disease, we extend our model by considering two types of infected persons: detectable and undetectable infected persons. Whether there is an outbreak is characterized by the spectral radius of a 2 X 2 matrix. If R 0 > 1, then the spectral radius of that matrix is greater than 1, and there is an outbreak. We plot the phase transition diagram of an outbreak and show that there are several countries on the verge of COVID-19 outbreaks on Mar. 2, 2020. To illustrate the effectiveness of social distancing, we analyze the independent cascade model for disease propagation in a configuration random network. We show two approaches of social distancing that can lead to a reduction of the effective reproduction number R e . |
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| AbstractList | In this paper, we conduct mathematical and numerical analyses for COVID-19. To predict the trend of COVID-19, we propose a time-dependent SIR model that tracks the transmission and recovering rate at time
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. Using the data provided by China authority, we show our one-day prediction errors are almost less than
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. The turning point and the total number of confirmed cases in China are predicted under our model. To analyze the impact of the undetectable infections on the spread of disease, we extend our model by considering two types of infected persons: detectable and undetectable infected persons. Whether there is an outbreak is characterized by the spectral radius of a
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matrix. If
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, then the spectral radius of that matrix is greater than 1, and there is an outbreak. We plot the phase transition diagram of an outbreak and show that there are several countries on the verge of COVID-19 outbreaks on Mar. 2, 2020. To illustrate the effectiveness of social distancing, we analyze the independent cascade model for disease propagation in a configuration random network. We show two approaches of social distancing that can lead to a reduction of the effective reproduction number
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. In this paper, we conduct mathematical and numerical analyses for COVID-19. To predict the trend of COVID-19, we propose a time-dependent SIR model that tracks the transmission and recovering rate at time [Formula: see text]. Using the data provided by China authority, we show our one-day prediction errors are almost less than [Formula: see text]. The turning point and the total number of confirmed cases in China are predicted under our model. To analyze the impact of the undetectable infections on the spread of disease, we extend our model by considering two types of infected persons: detectable and undetectable infected persons. Whether there is an outbreak is characterized by the spectral radius of a [Formula: see text] matrix. If [Formula: see text], then the spectral radius of that matrix is greater than 1, and there is an outbreak. We plot the phase transition diagram of an outbreak and show that there are several countries on the verge of COVID-19 outbreaks on Mar. 2, 2020. To illustrate the effectiveness of social distancing, we analyze the independent cascade model for disease propagation in a configuration random network. We show two approaches of social distancing that can lead to a reduction of the effective reproduction number [Formula: see text]. In this paper, we conduct mathematical and numerical analyses for COVID-19. To predict the trend of COVID-19, we propose a time-dependent SIR model that tracks the transmission and recovering rate at time [Formula: see text]. Using the data provided by China authority, we show our one-day prediction errors are almost less than [Formula: see text]. The turning point and the total number of confirmed cases in China are predicted under our model. To analyze the impact of the undetectable infections on the spread of disease, we extend our model by considering two types of infected persons: detectable and undetectable infected persons. Whether there is an outbreak is characterized by the spectral radius of a [Formula: see text] matrix. If [Formula: see text], then the spectral radius of that matrix is greater than 1, and there is an outbreak. We plot the phase transition diagram of an outbreak and show that there are several countries on the verge of COVID-19 outbreaks on Mar. 2, 2020. To illustrate the effectiveness of social distancing, we analyze the independent cascade model for disease propagation in a configuration random network. We show two approaches of social distancing that can lead to a reduction of the effective reproduction number [Formula: see text].In this paper, we conduct mathematical and numerical analyses for COVID-19. To predict the trend of COVID-19, we propose a time-dependent SIR model that tracks the transmission and recovering rate at time [Formula: see text]. Using the data provided by China authority, we show our one-day prediction errors are almost less than [Formula: see text]. The turning point and the total number of confirmed cases in China are predicted under our model. To analyze the impact of the undetectable infections on the spread of disease, we extend our model by considering two types of infected persons: detectable and undetectable infected persons. Whether there is an outbreak is characterized by the spectral radius of a [Formula: see text] matrix. If [Formula: see text], then the spectral radius of that matrix is greater than 1, and there is an outbreak. We plot the phase transition diagram of an outbreak and show that there are several countries on the verge of COVID-19 outbreaks on Mar. 2, 2020. To illustrate the effectiveness of social distancing, we analyze the independent cascade model for disease propagation in a configuration random network. We show two approaches of social distancing that can lead to a reduction of the effective reproduction number [Formula: see text]. In this paper, we conduct mathematical and numerical analyses for COVID-19. To predict the trend of COVID-19, we propose a time-dependent SIR model that tracks the transmission and recovering rate at time t. Using the data provided by China authority, we show our one-day prediction errors are almost less than 3%. The turning point and the total number of confirmed cases in China are predicted under our model. To analyze the impact of the undetectable infections on the spread of disease, we extend our model by considering two types of infected persons: detectable and undetectable infected persons. Whether there is an outbreak is characterized by the spectral radius of a 2 X 2 matrix. If R 0 > 1, then the spectral radius of that matrix is greater than 1, and there is an outbreak. We plot the phase transition diagram of an outbreak and show that there are several countries on the verge of COVID-19 outbreaks on Mar. 2, 2020. To illustrate the effectiveness of social distancing, we analyze the independent cascade model for disease propagation in a configuration random network. We show two approaches of social distancing that can lead to a reduction of the effective reproduction number R e . In this paper, we conduct mathematical and numerical analyses for COVID-19. To predict the trend of COVID-19, we propose a time-dependent SIR model that tracks the transmission and recovering rate at time [Formula Omitted]. Using the data provided by China authority, we show our one-day prediction errors are almost less than [Formula Omitted]. The turning point and the total number of confirmed cases in China are predicted under our model. To analyze the impact of the undetectable infections on the spread of disease, we extend our model by considering two types of infected persons: detectable and undetectable infected persons. Whether there is an outbreak is characterized by the spectral radius of a [Formula Omitted] matrix. If [Formula Omitted], then the spectral radius of that matrix is greater than 1, and there is an outbreak. We plot the phase transition diagram of an outbreak and show that there are several countries on the verge of COVID-19 outbreaks on Mar. 2, 2020. To illustrate the effectiveness of social distancing, we analyze the independent cascade model for disease propagation in a configuration random network. We show two approaches of social distancing that can lead to a reduction of the effective reproduction number [Formula Omitted]. |
| Author | Chang, Cheng-Shang Liu, Tzu-Hsuan Lu, Ping-En Chen, Yi-Cheng |
| AuthorAffiliation | Institute of Communications Engineering National Tsing Hua University 34881 Hsinchu 30013 Taiwan R.O.C |
| AuthorAffiliation_xml | – name: Institute of Communications Engineering National Tsing Hua University 34881 Hsinchu 30013 Taiwan R.O.C |
| Author_xml | – sequence: 1 givenname: Yi-Cheng surname: Chen fullname: Chen, Yi-Cheng email: yichengchen@gapp.nthu.edu.tw organization: Institute of Communications Engineering, National Tsing Hua University, Hsinchu, Taiwan R.O.C – sequence: 2 givenname: Ping-En orcidid: 0000-0002-1352-0983 surname: Lu fullname: Lu, Ping-En email: j94223@gmail.com organization: Institute of Communications Engineering, National Tsing Hua University, Hsinchu, Taiwan R.O.C – sequence: 3 givenname: Cheng-Shang orcidid: 0000-0002-5386-4756 surname: Chang fullname: Chang, Cheng-Shang email: cschang@ee.nthu.edu.tw organization: Institute of Communications Engineering, National Tsing Hua University, Hsinchu, Taiwan R.O.C – sequence: 4 givenname: Tzu-Hsuan surname: Liu fullname: Liu, Tzu-Hsuan email: carinaliu@gapp.nthu.edu.tw organization: Institute of Communications Engineering, National Tsing Hua University, Hsinchu, Taiwan R.O.C |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/37981959$$D View this record in MEDLINE/PubMed |
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| Copyright | IEEE 2020. Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2020 IEEE 2020. IEEE |
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| Keywords | COVID-19 herd immunity undetectable infection SARS-CoV-2 independent cascade time-dependent SIR model Coronavirus social distancing superspreader |
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| References | ref13 ref15 ref14 ref31 ref32 nesteruk (ref3) 0 (ref2) 2020 ref1 ref17 peng (ref5) 0 ref19 ref18 maier (ref7) 0 wyman (ref21) 2020 ref24 ref23 ganyani (ref25) 0 ref26 ref20 (ref12) 2020 ref22 althouse (ref33) 0 chen (ref27) 1999 ref28 ref8 (ref16) 2020 ref9 (ref30) 2020 ref4 ref6 hu (ref11) 0 pedregosa (ref29) 2011; 12 zeng (ref10) 0 |
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| Snippet | In this paper, we conduct mathematical and numerical analyses for COVID-19. To predict the trend of COVID-19, we propose a time-dependent SIR model that tracks... |
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| SubjectTerms | Coronavirus Coronaviruses COVID-19 Disease control Disease transmission Diseases Epidemics Government herd immunity Impact analysis independent cascade Mathematical analysis Mathematical model Matrix methods Numerical models Outbreaks Phase transitions Predictive models SARS-CoV-2 Social distancing Sociology Statistics superspreader Time dependence time-dependent SIR model undetectable infection Viral diseases |
| Title | A Time-Dependent SIR Model for COVID-19 With Undetectable Infected Persons |
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