Pharmacokinetic model based on multifactor uncertain differential equation

Z. Liu and Y. Yang

Applied Mathematics and Computation, 2021, vol. 392, issue C

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.

Keywords: Uncertain differential equations; Pharmacokinetics; Liu process; α-path; Uncertainty theory (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:392:y:2021:i:c:s0096300320306755

DOI: 10.1016/j.amc.2020.125722

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