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.

中文翻译：

---

基于多因素不确定微分方程的药代动力学模型

摘要 本文将经典药代动力学模型从确定性框架扩展到不确定性框架，以合理解释各种噪声，并应用不确定性微分方程理论对该模型进行分析。证明了药物浓度的逆不确定性分布可以通过常微分方程组得到。基于此结果，可以获得一些基本药代动力学指标的不确定性分布、预期值和置信区间等特性。对于不确定的药代动力学模型中的未知参数，给出了广义矩估计。一个数值例子将我们的方法与确定性方法进行了比较，并说明了我们方法的有效性和合理性。此外，所提出的方法应用于真实数据集。