A Study of Pharmacokinetic Model

The compartmental approach is an empirical procedure for pharmacokinetic modeling. This model has been used to derive many useful quantities by comparing the predicted values with actual data. However, in clinical operations, the resident time of a drug in the stomach may vary depending on the time for gastric emptying. The latter is a↵ected by food uptake, other drugs, placebos, and other factors. Moreover, real pharmacological processes are always exposed to influences that are not completely understood or for which it is not feasible to model explicitly. Ignoring these phenomena the modeling may a↵ect the estimation of PK/PD parameters and the derived conclusions.Therefore, there is an increasing need to extend the deterministic models to ones including a stochastic component. In order to get a more reliable analysis, in our study, we added a control vector to the Pharmacokinetic model, then used optimal control theory to analyze the modified model and find an equilibrium point; then, near the stationary point, we added white noise to the modified model and analyzed the stochastic di↵erential equation. We prove existence and uniqueness of the system and get an explicit solution of the SDE. *Presenter Qianning Liu Primary classification viiidynamical systems Secondary classification xvpharmacology 1