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Uncertain Population Model with Jumps

Author

Listed:
  • Caiwen Gao

    (School of Mathematics and Statistics, Shanxi Datong University, Datong 037009, China)

  • Zhiqiang Zhang

    (School of Mathematics and Statistics, Shanxi Datong University, Datong 037009, China)

  • Baoliang Liu

    (School of Mathematics and Statistics, Shanxi Datong University, Datong 037009, China)

Abstract

The uncertain population model (UPM), which has been proposed and studied, is a kind of population model driven by a Liu process that can only deal with continuous uncertain population systems. In reality, however, species systems may be suddenly shaken by earthquakes, tsunamis, epidemics, etc. The drastic changes lead to jumps in the population and make the sample path no longer continuous. In order to model the dramatic drifts embedded in an uncertain dynamic population system, this paper proposes a novel uncertain population model with jumps (UPMJ), which is described by a kind of uncertain differential equation with jumps (UDEJ). Then, the distribution function and the stability of solution for UPMJ are discussed based on uncertainty theory. Finally, a numerical example related to the transmission of Ebola virus is given to illustrate the characteristics of the distribution function and the stability of solution for UPMJ.

Suggested Citation

  • Caiwen Gao & Zhiqiang Zhang & Baoliang Liu, 2022. "Uncertain Population Model with Jumps," Mathematics, MDPI, vol. 10(13), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2265-:d:850756
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    References listed on IDEAS

    as
    1. Ziqiang Lu & Hongyan Yan & Yuanguo Zhu, 2019. "European option pricing model based on uncertain fractional differential equation," Fuzzy Optimization and Decision Making, Springer, vol. 18(2), pages 199-217, June.
    2. Jia, Lifen & Sheng, Yuhong, 2019. "Stability in distribution for uncertain delay differential equation," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 49-56.
    3. Gao, Rong, 2019. "Stability in mean for uncertain differential equation with jumps," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 15-22.
    4. Liu, Z. & Yang, Y., 2021. "Uncertain pharmacokinetic model based on uncertain differential equation," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    5. Jia, Lifen & Liu, Xueyong, 2021. "Optimal harvesting strategy based on uncertain logistic population model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    6. Kai Yao & Baoding Liu, 2020. "Parameter estimation in uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 1-12, March.
    7. Lu, Ziqiang & Zhu, Yuanguo & Li, Bo, 2019. "Critical value-based Asian option pricing model for uncertain financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 694-703.
    8. Liu, Z. & Yang, Y., 2021. "Pharmacokinetic model based on multifactor uncertain differential equation," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    Full references (including those not matched with items on IDEAS)

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