A linear uncertain pharmacokinetic model driven by Liu process

Abstract

There are inevitably dynamic noises in the pharmacokinetics, which can not be depicted well by deterministic methods. In addition, stochastic pharmacokinetic models under the framework of probability theory are valid under the premise that the distribution function (no matter how we get it) is close enough to the real frequency. However, due to the complexity and changeability of the world, economic and technological reasons, this premise can not be satisfied in some cases. Under these situations, this paper first deduces a linear uncertain pharmacokinetic model based on uncertain differential equations to rationally model dynamic noises. Several essential pharmacokinetic indexes are investigated. Generalized moment estimations for unknown parameters in this linear uncertain pharmacokinetic model are also given. A numerical example and two case studies using real data illustrate our method and compare the linear uncertain pharmacokinetic model driven by Liu process with deterministic pharmacokinetic model. As we can see, the linear uncertain pharmacokinetic model driven by Liu processes gives satisfactory results, and is suitable to model pharmacokinetics in reality.