Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Final and peak epidemic sizes for SEIR models with quarantine and isolation

1. Department of Mathematics, Purdue University, West Lafayette, IN 47907-1395

Two $SEIR$ models with quarantine and isolation are considered, in which the latent and infectious periods are assumed to have an exponential and gamma distribution, respectively. Previous studies have suggested (based on numerical observations) that a gamma distribution model (GDM) tends to predict a larger epidemic peak value and shorter duration than an exponential distribution model (EDM). By deriving analytic formulas for the maximum and final epidemic sizes of the two models, we demonstrate that either GDM or EDM may predict a larger epidemic peak or final epidemic size, depending on control measures. These formulas are helpful not only for understanding how model assumptions may affect the predictions, but also for confirming that it is important to assume realistic distributions of latent and infectious periods when the model is used for public health policy making.
  Article Metrics

Keywords disease control.; final epidemic size; peak epidemic size; infectious diseases; mathematical model

Citation: Z. Feng. Final and peak epidemic sizes for SEIR models with quarantine and isolation. Mathematical Biosciences and Engineering, 2007, 4(4): 675-686. doi: 10.3934/mbe.2007.4.675


This article has been cited by

  • 1. Fred Brauer, General compartmental epidemic models, Chinese Annals of Mathematics, Series B, 2010, 31, 3, 289, 10.1007/s11401-009-0454-1
  • 2. Jianquan Li, Yijun Lou, Characteristics of an epidemic outbreak with a large initial infection size, Journal of Biological Dynamics, 2016, 10, 1, 366, 10.1080/17513758.2016.1205223
  • 3. Jing-An Cui, Fangyuan Chen, Effects of isolation and slaughter strategies in different species on emerging zoonoses, Mathematical Biosciences and Engineering, 2017, 14, 5/6, 1119, 10.3934/mbe.2017058
  • 4. N. Sherborne, K. B. Blyuss, I. Z. Kiss, Dynamics of Multi-stage Infections on Networks, Bulletin of Mathematical Biology, 2015, 77, 10, 1909, 10.1007/s11538-015-0109-1
  • 5. Ping Yan, Zhilan Feng, Variability order of the latent and the infectious periods in a deterministic SEIR epidemic model and evaluation of control effectiveness, Mathematical Biosciences, 2010, 224, 1, 43, 10.1016/j.mbs.2009.12.007
  • 6. Xinxin Wang, Shengqiang Liu, Lin Wang, Weiwei Zhang, An Epidemic Patchy Model with Entry–Exit Screening, Bulletin of Mathematical Biology, 2015, 77, 7, 1237, 10.1007/s11538-015-0084-6
  • 7. Mohammad A. Safi, Mudassar Imran, Abba B. Gumel, Threshold dynamics of a non-autonomous SEIRS model with quarantine and isolation, Theory in Biosciences, 2012, 131, 1, 19, 10.1007/s12064-011-0148-6
  • 8. Fengqin Zhang, Jianquan Li, Jia Li, Epidemic characteristics of two classic SIS models with disease-induced death, Journal of Theoretical Biology, 2017, 424, 73, 10.1016/j.jtbi.2017.04.029
  • 9. Zhenyuan Guo, Lihong Huang, Xingfu Zou, Impact of discontinuous treatments on disease dynamics in an SIR epidemic model, Mathematical Biosciences and Engineering, 2011, 9, 1, 97, 10.3934/mbe.2012.9.97
  • 10. Yali Yang, Yiqun Li, Jianquan Li, Epidemic characteristics of two classic models and the dependence on the initial conditions, Mathematical Biosciences and Engineering, 2016, 13, 5, 999, 10.3934/mbe.2016027
  • 11. Marek Trawicki, Deterministic Seirs Epidemic Model for Modeling Vital Dynamics, Vaccinations, and Temporary Immunity, Mathematics, 2017, 5, 1, 7, 10.3390/math5010007
  • 12. Jingan Cui, Yanan Zhang, Zhilan Feng, Influence of non-homogeneous mixing on final epidemic size in a meta-population model, Journal of Biological Dynamics, 2018, 1, 10.1080/17513758.2018.1484186
  • 13. Qianqian Cui, Qiang Zhang, Zhipeng Qiu, Xiaomin Yang, Transmission Dynamics of an Epidemic Model with Vaccination, Treatment and Isolation, Bulletin of the Malaysian Mathematical Sciences Society, 2017, 10.1007/s40840-017-0519-3
  • 14. Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng, , Mathematical Models in Epidemiology, 2019, Chapter 4, 117, 10.1007/978-1-4939-9828-9_4
  • 15. Rosalyn J. Moran, Erik D. Fagerholm, Maell Cullen, Jean Daunizeau, Mark P. Richardson, Steven Williams, Federico Turkheimer, Rob Leech, Karl J. Friston, Estimating required ‘lockdown’ cycles before immunity to SARS-CoV-2: model-based analyses of susceptible population sizes, ‘S0’, in seven European countries, including the UK and Ireland, Wellcome Open Research, 2020, 5, 85, 10.12688/wellcomeopenres.15886.1

Reader Comments

your name: *   your email: *  

Copyright Info: 2007, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved