Geometric singular perturbation analysis of a dynamical target mediated drug disposition model

Kristian Uldall Kristiansen*

*Corresponding author for this work

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In this paper we present a mathematical analysis of a pharmacological ODE model for target mediated drug disposition (TMDD). It is known that solutions of this model undergo four qualitatively different phases. In this paper we provide a mathematical identification of these separate phases by viewing the TMDD model as a singular perturbed system. Our analysis is based on geometric singular perturbation theory and we believe that this approach systemizes-and sheds further light on-the scalings arguments used by previous authors. In particular, we present a novel description of the third phase through a distinguished solution of a nonlinear differential equation. We also describe the solution curve for large values of initial drug doses and recover, en route, a result by Aston et al. (J Math Biol 68(6):1453-1478, 2014) on rebounding using our alternative perturbation approach. Finally, from our main result we derive a new method for estimating the parameters of the system in the event that detailed data is available. Ideally our approach to the TMDD model should stimulate further research into applications of these methods to more complicated models in pharmacology.
Original languageEnglish
JournalJournal of Mathematical Biology
Issue number1
Pages (from-to)187-222
Number of pages36
Publication statusPublished - 2019


  • Geometric singular perturbation theory
  • Pharmacology
  • Target mediated drug disposition

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