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Pharmacokinetic model based on multifactor uncertain differential equation

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  • Liu, Z.
  • Yang, Y.

Abstract

This paper extends the classical pharmacokinetic model from a deterministic framework to an uncertain one to rationally explain various noises, and applies theory of uncertain differential equations to analyzing this model. It is proved that the inverse uncertainty distribution for the drug concentration can be obtained by a system of ordinary differential equations. Based on this result, properties such as uncertainty distributions, expected values, and confidence intervals for some essential pharmacokinetic indexes are obtained. For unknown parameters in the uncertain pharmacokinetic model, generalized moments estimations are given. A numerical example compares our methods with the deterministic method, and illustrates the effectiveness and rationality of our methods. Furthermore, the proposed methods are applied to a real dataset. Finally, the paradox of stochastic pharmacokinetic model is pointed out.

Suggested Citation

  • Liu, Z. & Yang, Y., 2021. "Pharmacokinetic model based on multifactor uncertain differential equation," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    • Handle: RePEc:eee:apmaco:v:392:y:2021:i:c:s0096300320306755
    DOI: 10.1016/j.amc.2020.125722
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    References listed on IDEAS

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    1. Xiangfeng Yang & Baoding Liu, 2019. "Uncertain time series analysis with imprecise observations," Fuzzy Optimization and Decision Making, Springer, vol. 18(3), pages 263-278, September.
    2. Xiangfeng Yang & Kai Yao, 2017. "Uncertain partial differential equation with application to heat conduction," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 379-403, September.
    3. Zhang, Yi & Gao, Jinwu & Huang, Zhiyong, 2017. "Hamming method for solving uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 331-341.
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    Cited by:

    1. Shen, Jiayu & Shi, Jianxin & Gao, Lingceng & Zhang, Qiang & Zhu, Kai, 2023. "Uncertain green product supply chain with government intervention," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 136-156.
    2. Jia, Lifen & Liu, Xueyong, 2021. "Optimal harvesting strategy based on uncertain logistic population model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Caiwen Gao & Zhiqiang Zhang & Baoliang Liu, 2022. "Uncertain Population Model with Jumps," Mathematics, MDPI, vol. 10(13), pages 1-12, June.
    4. Chen, Dan & Liu, Yang, 2023. "Uncertain Gordon-Schaefer model driven by Liu process," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    5. Liu, Zhe & Li, Xiaoyang & Kang, Rui, 2022. "Uncertain differential equation based accelerated degradation modeling," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    6. Liu, Z. & Yang, Y., 2021. "Selection of uncertain differential equations using cross validation," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    7. Tingqing Ye & Baoding Liu, 2023. "Uncertain hypothesis test for uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 22(2), pages 195-211, June.
    8. Liu, Zhe & Wang, Shihai & Liu, Bin & Kang, Rui, 2023. "Change point software belief reliability growth model considering epistemic uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

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