Pharmacokinetics is the study of the time course of drug concentrations in body compartments. The majority of drugs are eliminated at first order kinetics with a nonconstant elimination rate due to spontaneous erratic variations in the metabolic processes and individual difference. Noting the paradox of stochastic pharmacokinetic models, this paper proposes an uncertain pharmacokinetic model for mono-compartmental drugs administered with intravenous administration based on uncertain differential equations. Uncertainty distributions, expected values and confidence intervals of the half-life and the area under the curve are provided. For this method to achieve its full potential, this paper derives moment estimations for unknown parameters in this uncertain pharmacokinetic model. Finally a numerical example and a real data analysis illustrate our methods.

药代动力学是研究车厢内药物浓度随时间变化的过程。由于代谢过程中自发的不稳定变化和个体差异，大多数药物以一阶动力学被消除，消除速率不恒定。注意到随机药代动力学模型的悖论，本文提出了基于不确定微分方程的静脉注射单室药物的不确定药代动力学模型。提供了半衰期和曲线下面积的不确定度分布，期望值和置信区间。为了使这种方法发挥其全部潜力，本文推导了这种不确定的药代动力学模型中未知参数的矩估计。