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Analysis of Virus Transmission: A Stochastic Transition Model Representation of Epidemiological Models


  • Christian Gourieroux
  • Joann Jasiak


The growing literature on the transmission of COVID-19 relies on various dynamic SIR-type models (Susceptible-Infected-Recovered). For ease of comparison and specification testing, we introduce a common stochastic representation of the SIR-type epidemiological models. This representation is a discrete time transition model, which allows for classifying the epidemiological models with respect to the number of states (compartments) and their interpretation. Additionally, the (stochastic) transition model eliminates several limitations of the (deterministic) continuous time epidemiological models, which are pointed out in the paper. We show that when data on aggregate compartment counts are available, all discrete time SIR-type models admit a nonlinear (pseudo) state space representation and can be consistently estimated and updated from an extended Kalman filter.

Suggested Citation

  • Christian Gourieroux & Joann Jasiak, 2020. "Analysis of Virus Transmission: A Stochastic Transition Model Representation of Epidemiological Models," Annals of Economics and Statistics, GENES, issue 140, pages 1-26.
  • Handle: RePEc:adr:anecst:y:2020:i:140:p:1-26
    DOI: 10.15609/annaeconstat2009.140.0001

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    Cited by:

    1. Gourieroux, C. & Jasiak, J., 2023. "Time varying Markov process with partially observed aggregate data: An application to coronavirus," Journal of Econometrics, Elsevier, vol. 232(1), pages 35-51.
    2. M. Hashem Pesaran & Cynthia Fan Yang, 2022. "Matching theory and evidence on CovidÔÇÉ19 using a stochastic network SIR model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(6), pages 1204-1229, September.
    3. Sean Elliott & Christian Gourieroux, 2020. "Uncertainty on the Reproduction Ratio in the SIR Model," Papers 2012.11542,
    4. Jean-Paul Renne & Guillaume Roussellet & Gustavo Schwenkler, 2020. "Preventing COVID-19 Fatalities: State versus Federal Policies," Papers 2010.15263,, revised Dec 2020.
    5. Sean ELLIOTT & Christian GOURIEROUX, 2020. "Uncertainty on the Reproduction Ratio in the SIR Model," Working Papers 2020-31, Center for Research in Economics and Statistics.

    More about this item


    Covid-19; Epidemiological Model; SIR Model; Transition Model; State-Space Representation;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • I10 - Health, Education, and Welfare - - Health - - - General


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