Work

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

Year: 2026

Type: article

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.

Source: Boundary Value Problems

DOI: 10.1186/s13661-025-02170-z

Authors: Ahmed Maher, Rasha O. A. Taie, Mona G. A. Alwaleedy

Institutions: Assiut University, Taiz University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

SDG: Good health and well-being

Open Access status: gold

Estimated APC paid: $1,890