Asymptotic stability and optimal control for a stochastic two-compartment pharmacokinetic model

Abstract In this paper, we present a modified two-compartment model for intravenous pharmacokinetics that incorporates stochastic dynamics using optimal control. The objective of the control approach is to minimize the total administered drug quantity while ensuring its therapeutic efficacy. In this article, we apply optimal control only to the central compartment. We derive the necessary conditions for optimal control, including the adjoint equations, using the Hamiltonian approach and Pontryagin’s Maximum Principle. Moreover, sufficient conditions for asymptotic stability are investigated using Lyapunov’s theorem. Numerical simulations are conducted to illustrate our results.