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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. 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.
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    4. 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).
    5. 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.
    6. Xiaowei Chen & Jing Li & Chen Xiao & Peilin Yang, 2021. "Numerical solution and parameter estimation for uncertain SIR model with application to COVID-19," Fuzzy Optimization and Decision Making, Springer, vol. 20(2), pages 189-208, June.
    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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