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The stochastic SEIR model before extinction: Computational approaches

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  • Artalejo, J.R.
  • Economou, A.
  • Lopez-Herrero, M.J.

Abstract

We study a stochastic epidemic model of Susceptible-Exposed-Infective-Removed (SEIR) type and we quantify its behavior during an outbreak. More specifically, we model the epidemic by a continuous-time Markov chain and we develop efficient computational procedures for the distribution of the duration of an outbreak. We also study the evolution of the epidemic before its extinction using the ratio-of-expectations (RE) distribution for the number of individuals in the various classes of the model. The obtained results are illustrated by numerical examples including an application to an outbreak of Marburg hemorrhagic fever.

Suggested Citation

  • Artalejo, J.R. & Economou, A. & Lopez-Herrero, M.J., 2015. "The stochastic SEIR model before extinction: Computational approaches," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1026-1043.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:1026-1043
    DOI: 10.1016/j.amc.2015.05.141
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    References listed on IDEAS

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    1. van Doorn, Erik A. & Pollett, Philip K., 2013. "Quasi-stationary distributions for discrete-state models," European Journal of Operational Research, Elsevier, vol. 230(1), pages 1-14.
    2. Carol Y. Lin, 2008. "Modeling Infectious Diseases in Humans and Animals by KEELING, M. J. and ROHANI, P," Biometrics, The International Biometric Society, vol. 64(3), pages 993-993, September.
    3. Chris Groendyke & David Welch & David R. Hunter, 2011. "Bayesian Inference for Contact Networks Given Epidemic Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(3), pages 600-616, September.
    4. Luiz Hotta, 2010. "Bayesian Melding Estimation of a Stochastic SEIR Model," Mathematical Population Studies, Taylor & Francis Journals, vol. 17(2), pages 101-111.
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    Cited by:

    1. Lifen Jia & Wei Chen, 2021. "Uncertain SEIAR model for COVID-19 cases in China," Fuzzy Optimization and Decision Making, Springer, vol. 20(2), pages 243-259, June.
    2. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Asymptotic behavior of a stochastic delayed SEIR epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 870-882.
    3. Vasileios E. Papageorgiou, 2025. "Boosting epidemic forecasting performance with enhanced RNN-type models," Operational Research, Springer, vol. 25(3), pages 1-23, September.
    4. Antonio Gómez-Corral & Martín López-García & Maria Jesus Lopez-Herrero & Diana Taipe, 2020. "On First-Passage Times and Sojourn Times in Finite QBD Processes and Their Applications in Epidemics," Mathematics, MDPI, vol. 8(10), pages 1-25, October.
    5. Wanduku, Divine, 2017. "Complete global analysis of a two-scale network SIRS epidemic dynamic model with distributed delay and random perturbations," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 49-76.
    6. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Asymptotic behavior of a stochastic delayed HIV-1 infection model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 867-882.
    7. Dong, Yafang & Huo, Liang’an, 2024. "A multi-scale mathematical model of rumor propagation considering both intra- and inter-individual dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    8. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2017. "Asymptotic behavior of stochastic multi-group epidemic models with distributed delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 527-541.
    9. Sun, Shulin & Sun, Yaru & Zhang, Guang & Liu, Xinzhi, 2017. "Dynamical behavior of a stochastic two-species Monod competition chemostat model," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 153-170.
    10. Vasileios E. Papageorgiou & Georgios Vasiliadis & George Tsaklidis, 2025. "An Enhanced Epidemic Susceptible-Infected-Hospitalized-Recovered-Deceased (SIHRD) Stochastic Model with Emphasis on the Impact of Hospitalizations on Epidemic Evolution," Methodology and Computing in Applied Probability, Springer, vol. 27(3), pages 1-26, September.
    11. Kar, T.K. & Nandi, Swapan Kumar & Jana, Soovoojeet & Mandal, Manotosh, 2019. "Stability and bifurcation analysis of an epidemic model with the effect of media," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 188-199.

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