Open AccessUnderstanding the Behavior of Systems Pharmacology Models Using Mathematical Analysis of Differential Equations: Prolactin Modeling as a Case Study
Author(s) -
Bakshi S,
de Lange EC,
van der Graaf PH,
Danhof M,
Peletier LA
Publication year - 2016
Publication title -
cpt: pharmacometrics and systems pharmacology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.53
H-Index - 37
ISSN - 2163-8306
DOI - 10.1002/psp4.12098
Subject(s) - nonlinear system , stability (learning theory) , mathematical model , computer science , dynamical systems theory , bifurcation , differential equation , biological system , mathematics , control theory (sociology) , physics , artificial intelligence , mathematical analysis , machine learning , biology , statistics , control (management) , quantum mechanics
In this tutorial, we introduce basic concepts in dynamical systems analysis, such as phase‐planes, stability, and bifurcation theory, useful for dissecting the behavior of complex and nonlinear models. A precursor‐pool model with positive feedback is used to demonstrate the power of mathematical analysis. This model is nonlinear and exhibits multiple steady states, the stability of which is analyzed. The analysis offers insight into model behavior and suggests useful parameter regions, which simulations alone could not.