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Parameter estimation of stochastic SIR model driven by small Lévy noise with time-dependent periodic transmission

Author

Listed:
  • Terry Easlick

    (Université de Montréal)

  • Wei Sun

    (Concordia University)

Abstract

We investigate the parameter estimation and prediction of two forms of the stochastic SIR model driven by small Lévy noise with time-dependent periodic transmission. We present consistency and rate of convergence results for the least-squares estimators. We include simulation studies using the method of projected gradient descent.

Suggested Citation

  • Terry Easlick & Wei Sun, 2025. "Parameter estimation of stochastic SIR model driven by small Lévy noise with time-dependent periodic transmission," Statistical Inference for Stochastic Processes, Springer, vol. 28(1), pages 1-30, April.
    • Handle: RePEc:spr:sistpr:v:28:y:2025:i:1:d:10.1007_s11203-024-09322-5
    DOI: 10.1007/s11203-024-09322-5
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    References listed on IDEAS

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    1. Zhou, Yanli & Yuan, Sanling & Zhao, Dianli, 2016. "Threshold behavior of a stochastic SIS model with Le´vy jumps," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 255-267.
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    3. Guy, Romain & Larédo, Catherine & Vergu, Elisabeta, 2014. "Parametric inference for discretely observed multidimensional diffusions with small diffusion coefficient," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 51-80.
    4. Mikael Jagan & Michelle S deJonge & Olga Krylova & David J D Earn, 2020. "Fast estimation of time-varying infectious disease transmission rates," PLOS Computational Biology, Public Library of Science, vol. 16(9), pages 1-39, September.
    5. Jiafeng Pan & Alison Gray & David Greenhalgh & Xuerong Mao, 2014. "Parameter estimation for the stochastic SIS epidemic model," Statistical Inference for Stochastic Processes, Springer, vol. 17(1), pages 75-98, April.
    6. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "A stochastic SIRS epidemic model with logistic growth and general nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    7. Masayuki Uchida, 2004. "Estimation for Discretely Observed Small Diffusions Based on Approximate Martingale Estimating Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(4), pages 553-566, December.
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