Hybrid stochastic differential systems in pharmacokinetics

Abstract

Abstract Modelling patient medication poor compliance combined with the inherent uncertainty in a bioavailability trial leads recognizably to the fact that plasma concentration-time curve must be treated as a random process. We suggest for modelling a general class of hybrid stochastic differential systems (HSDS). Roughly speaking, a HSDS is a piecewise diffusion process with jumps of two types: spontaneous and predictable. The essential tasks for us afterwards are to identify the model ingredients and to derive its bearings; of interest are a couple of operators associated to every Markov process: the generating operator and the Fokker–Planck operator. The model induces a Fokker–Planck–Kolmogorov equation along with moment equations, and computations based on direct solutions of the latter make it possible to study the variability of the concentration around its mean as compared to the full compliance case and to assess the effect of some parameters such as the intake and elimination rates.