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SIR-Type Epidemic Models as Block-Structured Markov Processes

Author

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  • Claude Lefèvre

    (Université Libre de Bruxelles)

  • Matthieu Simon

    (University of Melbourne)

Abstract

This paper proposes a block-structured Markov process to describe the spread of epidemics of Susceptible-Infected-Removed (SIR) type. Our purpose is to determine the distribution of the final state of the process and of some other interesting measures of the dimension of the epidemic. The followed modeling approach proves to be simple and systematic. Its flexibility is underlined by the presentation of several specific models that extend the classical general epidemic. Finally, two numerical examples illustrate some of the results obtained.

Suggested Citation

  • Claude Lefèvre & Matthieu Simon, 2020. "SIR-Type Epidemic Models as Block-Structured Markov Processes," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 433-453, June.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:2:d:10.1007_s11009-019-09710-y
    DOI: 10.1007/s11009-019-09710-y
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    References listed on IDEAS

    as
    1. Runhuan Feng & Jose Garrido, 2011. "Actuarial Applications of Epidemiological Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(1), pages 112-136.
    2. Asmussen, Soren & Avram, Florin & Usabel, Miguel, 2002. "Erlangian Approximations for Finite-Horizon Ruin Probabilities," ASTIN Bulletin, Cambridge University Press, vol. 32(2), pages 267-281, November.
    3. Picard, Philippe & Lefèvre, Claude, 1993. "Distribution of the final state and severity of epidemics with fatal risk," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 277-294, November.
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    Cited by:

    1. 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.
    2. Xiaowei Chen & Wing Fung Chong & Runhuan Feng & Linfeng Zhang, 2020. "Pandemic risk management: resources contingency planning and allocation," Papers 2012.03200, arXiv.org.
    3. Gómez-Corral, A. & Lopez-Herrero, M.J. & Taipe, D., 2023. "A Markovian epidemic model in a resource-limited environment," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    4. André de Palma & Nathalie Picard & Stef Proost, 2021. "SCARE: when Economics meets Epidemiology with COVID-19, first wave," THEMA Working Papers 2021-10, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    5. Chen, Xiaowei & Chong, Wing Fung & Feng, Runhuan & Zhang, Linfeng, 2021. "Pandemic risk management: Resources contingency planning and allocation," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 359-383.
    6. André de Palma & Nathalie Picard & Stef Proost, 2020. "SCARE: When Economics Meets Epidemiology with Covid-19," CESifo Working Paper Series 8573, CESifo.

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