TITLE:
Stability and Hopf Bifurcation of a Target-Mediated Drug Disposition Model
AUTHORS:
Tingyuan Zhao, Xin Li, Longge Su, Yan Yan
KEYWORDS:
TMDD Model, Stability, Hopf Bifurcation, Lyapunov Index
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.12,
December
16,
2025
ABSTRACT: In this paper, we study a three-dimensional target-mediated drug disposition model consisted of the drugs (ligands), targets (receptors) and drug-target (ligand-receptor) complexes. In this model, as the important drug administration method, a constant-rate intravenous continuous injection of the drugs is considered. Additionally, based on the nonlinear metabolism characteristics of drugs in human body, the drug reduction is described by the Michaelis-Menten equation. Firstly, the local stability of the positive equilibrium is investigated using the Routh-Hurwitz criterion. Then, by choosing the association rate of drugs and targets, which determines the effectiveness of drug binding to the target, as the bifurcation parameter, the existence conditions of Hopf bifurcation around the positive equilibrium are established. Finally, the stability of the bifurcating periodic solutions is also discussed by applying the Lyapunov index.