On the characteristic equation λ = α1 + (α2 + α3λ)e(-λ) and its use in the context of a cell population model

Odo Diekmann; Philipp Getto; Yukihiko Nakata

doi:10.1007/s00285-015-0918-8

On the characteristic equation λ = α1 + (α2 + α3λ)e(-λ) and its use in the context of a cell population model

J Math Biol. 2016 Mar;72(4):877-908. doi: 10.1007/s00285-015-0918-8. Epub 2015 Aug 6.

Authors

Odo Diekmann¹, Philipp Getto², Yukihiko Nakata³

Affiliations

¹ Mathematical Institute, University of Utrecht, Utrecht, The Netherlands.
² TU Dresden, Fachrichtung Mathematik, Institut für Analysis, 01062, Dresden, Germany.
³ Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan. [email protected].

Abstract

In this paper we characterize the stability boundary in the (α1, α2)-plane, for fixed α3 with −1 < α3 < +1, for the characteristic equation from the title. Subsequently we describe a nonlinear cell population model involving quiescence and show that this characteristic equation governs the (in)stability of the nontrivial steady state. By relating the parameters of the cell model to the αi we are able to derive some biological conclusions.

Keywords: 34K20; 37N25; 45D05; 65L03; 92D25.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Cell Cycle Checkpoints
Cell Growth Processes*
Cell Proliferation
Mathematical Concepts
Models, Biological*
Nonlinear Dynamics