{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,10]],"date-time":"2025-09-10T21:36:23Z","timestamp":1757540183410,"version":"3.37.3"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2021,3,24]],"date-time":"2021-03-24T00:00:00Z","timestamp":1616544000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,3,24]],"date-time":"2021-03-24T00:00:00Z","timestamp":1616544000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100019033","name":"Key Research and Development Program of Liaoning Province","doi-asserted-by":"crossref","award":["2019JH2\/10100019"],"award-info":[{"award-number":["2019JH2\/10100019"]}],"id":[{"id":"10.13039\/501100019033","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["N181606001, N2016011 and N2024005-1"],"award-info":[{"award-number":["N181606001, N2016011 and N2024005-1"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014718","name":"Innovative Research Group Project of the National Natural Science Foundation of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100014718","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Dyn Games Appl"],"published-print":{"date-parts":[[2021,12]]},"DOI":"10.1007\/s13235-021-00382-3","type":"journal-article","created":{"date-parts":[[2021,3,24]],"date-time":"2021-03-24T11:03:56Z","timestamp":1616583836000},"page":"892-914","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Modeling COVID-19 Pandemic with Hierarchical Quarantine and Time Delay"],"prefix":"10.1007","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4471-0026","authenticated-orcid":false,"given":"Wei","family":"Yang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,3,24]]},"reference":[{"issue":"7248","key":"382_CR1","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1016\/S0140-6736(66)92364-6","volume":"287","author":"DA Tyrrell","year":"1966","unstructured":"Tyrrell DA, Bynoe ML (1966) Cultivation of viruses from a high proportion of patients with colds. Lancet 287(7248):76\u201377","journal-title":"Lancet"},{"unstructured":"https:\/\/www.who.int\/emergencies\/diseases\/novel-coronavirus-2019\/events-as-they-happen","key":"382_CR2"},{"issue":"4305","key":"382_CR3","first-page":"733","volume":"1","author":"WH Hamer","year":"1906","unstructured":"Hamer WH (1906) Epidemic disease in England\u2014the evidence of variety and of persistency of type. Lancet 1(4305):733\u2013739","journal-title":"Lancet"},{"key":"382_CR4","volume-title":"The prevention of malaria","author":"R Ross","year":"1911","unstructured":"Ross R (1911) The prevention of malaria. Murray, London"},{"issue":"772","key":"382_CR5","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1098\/rspa.1927.0118","volume":"115","author":"WO Kermack","year":"1927","unstructured":"Kermack WO, McKendrick AG (1927) Contributions to the mathematical theory of epidemics. Proc R Soc London Series A 115(772):700\u2013721","journal-title":"Proc R Soc London Series A"},{"issue":"1","key":"382_CR6","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1016\/j.jmaa.2006.01.055","volume":"325","author":"N Dalal","year":"2007","unstructured":"Dalal N, Greenhalgh D, Mao X (2007) A stochastic model of AIDS and condom use. J Math Anal Appl 325(1):36\u201353","journal-title":"J Math Anal Appl"},{"issue":"3","key":"382_CR7","doi-asserted-by":"publisher","first-page":"876","DOI":"10.1137\/10081856X","volume":"71","author":"A Gray","year":"2011","unstructured":"Gray A, Greenhalgh D, Hu L, Mao X, Pan J (2011) A stochastic differential equation SIS epidemic model. SIAM J Appl Math 71(3):876\u2013902","journal-title":"SIAM J Appl Math"},{"key":"382_CR8","doi-asserted-by":"publisher","first-page":"59","DOI":"10.15388\/NA.16.1.14115","volume":"16","author":"A Lahrouz","year":"2011","unstructured":"Lahrouz A, Omari L, Kiouach D (2011) Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model. Nonlinear Anal Model Control 16:59\u201376","journal-title":"Nonlinear Anal Model Control"},{"key":"382_CR9","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1016\/j.physa.2005.02.057","volume":"354","author":"E Tornatore","year":"2005","unstructured":"Tornatore E, Buccellato SM, Vetro P (2005) Stability of a stochastic SIR system. Phys A 354:111\u2013126","journal-title":"Phys A"},{"key":"382_CR10","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1016\/j.plrev.2016.07.005","volume":"18","author":"G Chowell","year":"2016","unstructured":"Chowell G, Sattenspiel L, Bansal S, Viboud C (2016) Mathematical models to characterize early epidemic growth: a Review. Phys Life Rev 18:66\u201397","journal-title":"Phys Life Rev"},{"key":"382_CR11","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1186\/1741-7015-9-87","volume":"9","author":"J Stehle","year":"2011","unstructured":"Stehle J, Voirin N, Barrat A et al (2011) Simulation of an SEIR infectious disease model on the dynamic contact network of conference attendees. BMC Med 9:87","journal-title":"BMC Med"},{"key":"382_CR12","doi-asserted-by":"publisher","DOI":"10.1093\/cid\/ciaa325","author":"JF Chan","year":"2020","unstructured":"Chan JF, Zhang AJ, Yuan S, Poon VK et al (2020) Simulation of the clinical and pathological manifestations of coronavirus disease 2019 (COVID-19) in golden Syrian hamster model: implications for disease pathogenesis and transmissibility. Clin Infect Dis. https:\/\/doi.org\/10.1093\/cid\/ciaa325","journal-title":"Clin Infect Dis"},{"key":"382_CR13","doi-asserted-by":"publisher","first-page":"2842","DOI":"10.3934\/mbe.2020158","volume":"17","author":"J Tian","year":"2020","unstructured":"Tian J, Wu J, Bao Y et al (2020) Modeling analysis of COVID-19 based on morbidity data in Anhui, China. Math Biosci Eng 17:2842\u20132852","journal-title":"Math Biosci Eng"},{"issue":"4","key":"382_CR14","doi-asserted-by":"publisher","first-page":"2781","DOI":"10.3934\/mbe.2020152","volume":"17","author":"C Dai","year":"2020","unstructured":"Dai C, Yang J, Wang K (2020) Evaluation of prevention and control interventions and its impact on the epidemic of coronavirus disease 2019 in Chongqing and Guizhou Provinces. Math Biosci Eng 17(4):2781\u20132791","journal-title":"Math Biosci Eng"},{"key":"382_CR15","doi-asserted-by":"publisher","DOI":"10.1016\/S2468-2667(20)30073-6","author":"K Prem","year":"2020","unstructured":"Prem K, Liu Y, Russell TW, Kucharski AJ, Eggo RM, Davies N (2020) Centre for the mathematical modelling of infectious diseases COVID-19 working group, the effect of control strategies to reduce social mixing on outcomes of the COVID-19 epidemic in Wuhan, China: a modelling study. Lancet F Health. https:\/\/doi.org\/10.1016\/S2468-2667(20)30073-6","journal-title":"Lancet F Health"},{"key":"382_CR16","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1007\/s40484-020-0199-0","volume":"8","author":"S Zhao","year":"2020","unstructured":"Zhao S, Chen H (2020) Modeling the epidemic dynamics and control of COVID-19 outbreak in China. Quant Biol 8:11\u201319","journal-title":"Quant Biol"},{"key":"382_CR17","first-page":"248","volume":"5","author":"B Tang","year":"2020","unstructured":"Tang B, Bragazzi NL, Li Q, Tang S, Xiao Y, Wu J (2020) An updated estimation of the risk of transmission of the novel coronavirus (2019-nCov). Infect Dis Model 5:248\u2013255","journal-title":"Infect Dis Model"},{"issue":"1","key":"382_CR18","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1186\/s40249-020-00640-3","volume":"9","author":"TM Chen","year":"2020","unstructured":"Chen TM, Rui J, Wang QP, Zhao ZY, Cui JA, Yin L (2020) A mathematical model for simulating the phase-based transmissibility of a novel coronavirus. Infect Dis Poverty 9(1):24\u201324","journal-title":"Infect Dis Poverty"},{"key":"382_CR19","doi-asserted-by":"publisher","DOI":"10.1038\/s41421-020-0148-0","author":"H Wang","year":"2020","unstructured":"Wang H, Wang Z, Dong Y (2020) Phase-adjusted estimation of the number of coronavirus disease 2019 cases in Wuhan, China. Cell Discov. https:\/\/doi.org\/10.1038\/s41421-020-0148-0","journal-title":"Cell Discov"},{"issue":"10","key":"382_CR20","doi-asserted-by":"publisher","first-page":"1995","DOI":"10.1002\/jmv.25939","volume":"92","author":"T Sun","year":"2020","unstructured":"Sun T, Weng D (2020) Estimating the effects of asymptomatic and imported patients on COVID-19 epidemic using mathematical modeling. J Med Virol 92(10):1995\u20132003","journal-title":"J Med Virol"},{"doi-asserted-by":"crossref","unstructured":"Shao P, Shan Y (2020) Beware of asymptomatic transmission: Study on 2019 nCoV prevention and control measures based on extended SEIR model. bioRxiv","key":"382_CR21","DOI":"10.1101\/2020.01.28.923169"},{"key":"382_CR22","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/j.amc.2014.11.107","volume":"252","author":"L Li","year":"2015","unstructured":"Li L (2015) Bifurcation and chaos in a discrete physiological control system. Appl Math Comput 252:397\u2013404","journal-title":"Appl Math Comput"},{"issue":"6","key":"382_CR23","doi-asserted-by":"publisher","first-page":"1194","DOI":"10.1080\/00207721.2016.1244308","volume":"48","author":"Q Din","year":"2017","unstructured":"Din Q (2017) Global stability and Neimark-Sacker bifurcation of a host-parasitoid model. Int J Syst Sci 48(6):1194\u20131202","journal-title":"Int J Syst Sci"},{"key":"382_CR24","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.amc.2016.07.029","volume":"292","author":"C Huang","year":"2017","unstructured":"Huang C, Cao J, Xiao M, Alsaedi A, Hayat T (2017) Bifurcations in a delayed fractional complex-valued neural network. Appl Math Comput 292:210\u2013227","journal-title":"Appl Math Comput"},{"key":"382_CR25","first-page":"1","volume":"2012","author":"T Dong","year":"2012","unstructured":"Dong T, Liao X, Li H (2012) Stability and hopf bifurcation in a computer virus model with multistate antivirus. Abstr Appl Anal 2012:1\u201316","journal-title":"Abstr Appl Anal"},{"issue":"1","key":"382_CR26","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1016\/j.chaos.2011.10.003","volume":"45","author":"J Ren","year":"2012","unstructured":"Ren J, Yang XF, Yang LX (2012) A delayed computer virus propagation model and its dynamics. Chaos Solitons Fractals 45(1):74\u201379","journal-title":"Chaos Solitons Fractals"},{"issue":"3","key":"382_CR27","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1016\/j.mcm.2010.02.044","volume":"52","author":"S Wang","year":"2010","unstructured":"Wang S, Liu QM, Yu XF (2010) Bifurcation analysis of a model for network worm propagation with time delay. Math Comput Model 52(3):435\u2013447","journal-title":"Math Comput Model"},{"issue":"12","key":"382_CR28","doi-asserted-by":"publisher","first-page":"5117","DOI":"10.1016\/j.cnsns.2012.05.030","volume":"17","author":"Q Zhu","year":"2012","unstructured":"Zhu Q, Yang XF, Ren J (2012) Modeling and analysis of the spread of computer virus. Commun Nonlinear Sci Numer Simul 17(12):5117\u20135124","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"5627","key":"382_CR29","doi-asserted-by":"publisher","first-page":"1966","DOI":"10.1126\/science.1086616","volume":"300","author":"M Lipsitch","year":"2003","unstructured":"Lipsitch M, Cohen T, Cooper B et al (2003) Transmission dynamics and control of severe acute respiratory syndrome. Science 300(5627):1966\u20131970","journal-title":"Science"},{"issue":"10223","key":"382_CR30","doi-asserted-by":"publisher","first-page":"514","DOI":"10.1016\/S0140-6736(20)30154-9","volume":"395","author":"JF Chan","year":"2020","unstructured":"Chan JF, Yuan S, Kok K et al (2020) A familial cluster of pneumonia associated with the 2019 novel coronavirus indicating person-to-person transmission: a study of a family cluster. Lancet 395(10223):514\u2013523","journal-title":"Lancet"},{"key":"382_CR31","first-page":"170","volume":"362","author":"Z Cao","year":"2020","unstructured":"Cao Z, Zhang Q, Lu X et al (2020) Incorporating human movement data to improve epidemiological estimates for 2019-nCoV. MedRxiv 362:170","journal-title":"MedRxiv"},{"unstructured":"Ireland\u2019s Health Services (2020) Health Care Worker Information (PDF). Retrieved March 27","key":"382_CR32"},{"issue":"6","key":"382_CR33","doi-asserted-by":"publisher","first-page":"1000291","DOI":"10.1371\/journal.pmed.1000291","volume":"7","author":"M Kretzschmar","year":"2010","unstructured":"Kretzschmar M, Teunis PF, Pebody RG (2010) Incidence and reproduction numbers of pertussis: estimates from serological and social contact data in five European countries. PLOS Med 7(6):1000291","journal-title":"PLOS Med"},{"issue":"6865","key":"382_CR34","doi-asserted-by":"publisher","first-page":"748","DOI":"10.1038\/414748a","volume":"414","author":"R Gani","year":"2001","unstructured":"Gani R, Leach S (2001) Transmission potential of smallpox in contemporary populations. Nature 414(6865):748\u2013751","journal-title":"Nature"},{"issue":"1","key":"382_CR35","doi-asserted-by":"publisher","first-page":"291","DOI":"10.3390\/ijerph7010291","volume":"7","author":"H Nishiura","year":"2010","unstructured":"Nishiura H (2010) Correcting the actual reproduction number: a simple method to estimate R0 from early epidemic growth data. Int J Environ Res Public Health 7(1):291\u2013302","journal-title":"Int J Environ Res Public Health"},{"issue":"6","key":"382_CR36","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1093\/aje\/kwh255","volume":"160","author":"J Wallinga","year":"2004","unstructured":"Wallinga J, Teunis P (2004) Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures. Am J Epidemiol 160(6):509\u2013516","journal-title":"Am J Epidemiol"},{"issue":"4","key":"382_CR37","doi-asserted-by":"publisher","first-page":"2000058","DOI":"10.2807\/1560-7917.ES.2020.25.4.2000058","volume":"25","author":"J Riou","year":"2020","unstructured":"Riou J, Althaus CL (2020) Pattern of early human-to-human transmission of Wuhan 2019 novel coronavirus (2019-nCoV), December 2019 to January 2020. Eurosurveillance 25(4):2000058","journal-title":"Eurosurveillance"},{"doi-asserted-by":"crossref","unstructured":"Liu T, Hu J, Kang M, Lin L (2020) Time-varying transmission dynamics of novel coronavirus pneumonia in China. bioRxiv 2: 79","key":"382_CR38","DOI":"10.1101\/2020.01.25.919787"},{"issue":"7","key":"382_CR39","first-page":"1258","volume":"10","author":"JM Read","year":"2020","unstructured":"Read JM, Bridgen JR, Cummings DA et al (2020) Novel coronavirus 2019-nCoV: early estimation of epidemiological parameters and epidemic predictions. MedRxiv 10(7):1258","journal-title":"MedRxiv"},{"issue":"4","key":"382_CR40","doi-asserted-by":"publisher","first-page":"506","DOI":"10.1038\/s41591-020-0822-7","volume":"26","author":"JT Wu","year":"2020","unstructured":"Wu JT, Leung K, Bushman M et al (2020) Estimating clinical severity of COVID-19 from the transmission dynamics in Wuhan, China. Nat Med 26(4):506\u2013510","journal-title":"Nat Med"},{"key":"382_CR41","doi-asserted-by":"publisher","DOI":"10.1371\/currents.outbreaks.91afb5e0f279e7f29e7056095255b288","author":"CL Althaus","year":"2014","unstructured":"Althaus CL (2014) Estimating the reproduction number of ebola virus (EBOV) during the 2014 outbreak in West Africa. PLOS Curr. https:\/\/doi.org\/10.1371\/currents.outbreaks.91afb5e0f279e7f29e7056095255b288","journal-title":"PLOS Curr"},{"issue":"1","key":"382_CR42","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1186\/1741-7015-7-30","volume":"7","author":"BJ Coburn","year":"2009","unstructured":"Coburn BJ, Wagner BG, Blower S (2009) Modeling influenza epidemics and epidemics: insights into the future of swine flu (H1N1). BMC Med 7(1):30\u201330","journal-title":"BMC Med"},{"key":"382_CR43","first-page":"210","volume-title":"Theory and application of Hopf bifurcation","author":"B Hassard","year":"1981","unstructured":"Hassard B, Kazarino D, Wan Y (1981) Theory and application of Hopf bifurcation. Cambridge University Press, Cambridge, pp 210\u2013211"},{"key":"382_CR44","doi-asserted-by":"publisher","first-page":"860","DOI":"10.1126\/science.abb5793","volume":"368","author":"SM Kissler","year":"2020","unstructured":"Kissler SM, Tedijanto C, Goldstein E et al (2020) Projecting the transmission dynamics of SARS-CoV-2 through the post epidemic period. Science 368:860\u2013868","journal-title":"Science"},{"key":"382_CR45","doi-asserted-by":"publisher","DOI":"10.1002\/9781118762783","volume-title":"Propagation dynamics on complex networks: models, methods and stability analysis","author":"X Fu","year":"2014","unstructured":"Fu X, Small M, Chen G (2014) Propagation dynamics on complex networks: models, methods and stability analysis. Higher Education Press, Beijing"}],"container-title":["Dynamic Games and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13235-021-00382-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13235-021-00382-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13235-021-00382-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,1]],"date-time":"2023-11-01T00:01:19Z","timestamp":1698796879000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13235-021-00382-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,24]]},"references-count":45,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["382"],"URL":"https:\/\/doi.org\/10.1007\/s13235-021-00382-3","relation":{},"ISSN":["2153-0785","2153-0793"],"issn-type":[{"type":"print","value":"2153-0785"},{"type":"electronic","value":"2153-0793"}],"subject":[],"published":{"date-parts":[[2021,3,24]]},"assertion":[{"value":"10 March 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 March 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declaration"}},{"value":"I declare that there is no conflict of interest regarding the publication of this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}