Pharmacokinetic model for extravascular administration based on uncertain differential equation

Pharmacokinetics studies the time course of drug concentration in body compartments, and one of the commonly used methods of administration is extravascular administration. Undoubtedly, biological systems are subject to various internal and external noises that change over time. To rationally deal with these dynamic noises, this paper deduces a pharmacokinetic model for extravascular administration using uncertain differential equations for the first time. Some essential pharmacokinetic indexes such as drug concentration, area under the curve, and maximum drug concentration are investigated. Based on the three basic principles of reliability science, i.e., margin-based reliable principle, eternal degradation principle and uncertainty principle, the belief reliability for drug is investigated. The minimum cover estimation for the set of unknown parameters in this uncertain pharmacokinetic model is provided. Numerical example and a real data analysis illustrate our method in detail. Finally, the paradox of a stochastic pharmacokinetic model is presented. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.