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Numerical solution and parameter estimation for uncertain SIR model with application to COVID-19

Author

Listed:
  • Xiaowei Chen

    (Nankai University)

  • Jing Li

    (Nankai University)

  • Chen Xiao

    (Nankai University)

  • Peilin Yang

    (Nankai University)

Abstract

Developing algorithms for solving high-dimensional uncertain differential equations has been an exceedingly difficult task. This paper presents an $$\alpha $$ α -path-based approach that can handle the proposed high-dimensional uncertain SIR model. We apply the $$\alpha $$ α -path-based approach to calculating the uncertainty distributions and related expected values of the solutions. Furthermore, we employ the method of moments to estimate parameters and design a numerical algorithm to solve them. This model is applied to describing the development trend of COVID-19 using infected and recovered data of Hubei province. The results indicate that lockdown policy achieves almost 100% efficiency after February 13, 2020, which is consistent with the existing literatures. The high-dimensional $$\alpha $$ α -path-based approach opens up new possibilities in solving high-dimensional uncertain differential equations and new applications.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:fuzodm:v:20:y:2021:i:2:d:10.1007_s10700-020-09342-9
    DOI: 10.1007/s10700-020-09342-9
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    References listed on IDEAS

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    1. Kai Yao & Baoding Liu, 2020. "Parameter estimation in uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 1-12, March.
    2. Zhiming Li & Zhidong Teng, 2019. "Analysis of uncertain SIS epidemic model with nonlinear incidence and demography," Fuzzy Optimization and Decision Making, Springer, vol. 18(4), pages 475-491, December.
    3. Yang, Xiangfeng & Liu, Yuhan & Park, Gyei-Kark, 2020. "Parameter estimation of uncertain differential equation with application to financial market," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Jayson S. Jia & Xin Lu & Yun Yuan & Ge Xu & Jianmin Jia & Nicholas A. Christakis, 2020. "Population flow drives spatio-temporal distribution of COVID-19 in China," Nature, Nature, vol. 582(7812), pages 389-394, June.
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    Cited by:

    1. Gao, Yin & Gao, Jinwu & Yang, Xiangfeng, 2022. "The almost sure stability for uncertain delay differential equations based on normal lipschitz conditions," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    2. Shami, Labib & Lazebnik, Teddy, 2022. "Economic aspects of the detection of new strains in a multi-strain epidemiological–mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    3. Liu He & Yuanguo Zhu & Yajing Gu, 2023. "Nonparametric estimation for uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 22(4), pages 697-715, December.
    4. Tang, Han & Yang, Xiangfeng, 2021. "Uncertain chemical reaction equation," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    5. Zhangbo Yang & Jiahao Zhang & Shanxing Gao & Hui Wang, 2022. "Complex Contact Network of Patients at the Beginning of an Epidemic Outbreak: An Analysis Based on 1218 COVID-19 Cases in China," IJERPH, MDPI, vol. 19(2), pages 1-17, January.
    6. Chen, Dan & Liu, Yang, 2023. "Uncertain Gordon-Schaefer model driven by Liu process," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    7. Liu He & Yuanguo Zhu & Ziqiang Lu, 2023. "Parameter estimation for uncertain fractional differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 22(1), pages 103-122, March.
    8. Yang Liu & Baoding Liu, 2022. "Residual analysis and parameter estimation of uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 21(4), pages 513-530, December.
    9. Vahdani, Behnam & Mohammadi, Mehrdad & Thevenin, Simon & Meyer, Patrick & Dolgui, Alexandre, 2023. "Production-sharing of critical resources with dynamic demand under pandemic situation: The COVID-19 pandemic," Omega, Elsevier, vol. 120(C).
    10. Farshid Mehrdoust & Idin Noorani & Wei Xu, 2023. "Uncertain energy model for electricity and gas futures with application in spark-spread option price," Fuzzy Optimization and Decision Making, Springer, vol. 22(1), pages 123-148, March.

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