Stability analysis of a renewal equation for cell population dynamics with quiescence

Tomás Alarcón; Philipp Getto; Yukihiko Nakata

doi:10.1137/130940438

Stability analysis of a renewal equation for cell population dynamics with quiescence

Tomás Alarcón, Philipp Getto, Yukihiko Nakata

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Abstract

© 2014 Society for Industrial and Applied Mathematics We propose a model to analyze the dynamics of interacting proliferating and quiescent cell populations. The model includes age dependence of cell division, transitions between the two subpopulations, and regulation of the recruitment of quiescent cells. We formulate the model as a pair of renewal equations and apply a rather recent general result to prove that (in)stability of equilibria can be analyzed by locating roots of characteristic equations. We are led to a parameter plane analysis of a characteristic equation, which has not been analyzed in this way so far. We conclude with how quiescence of cells as well as two submodels for cell division may influence the possibility of destabilization via oscillations.

Original language	English
Pages (from-to)	1266-1297
Journal	SIAM Journal on Applied Mathematics
Volume	74
Issue number	4
DOIs	https://doi.org/10.1137/130940438
Publication status	Published - 1 Jan 2014

Keywords

Age structure
Cell population model
Characteristic equation
Hopf bifurcation
Quiescence
Renewal equation

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Alarcón, T., Getto, P., & Nakata, Y. (2014). Stability analysis of a renewal equation for cell population dynamics with quiescence. SIAM Journal on Applied Mathematics, 74(4), 1266-1297. https://doi.org/10.1137/130940438

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AU - Nakata, Yukihiko

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N2 - © 2014 Society for Industrial and Applied Mathematics We propose a model to analyze the dynamics of interacting proliferating and quiescent cell populations. The model includes age dependence of cell division, transitions between the two subpopulations, and regulation of the recruitment of quiescent cells. We formulate the model as a pair of renewal equations and apply a rather recent general result to prove that (in)stability of equilibria can be analyzed by locating roots of characteristic equations. We are led to a parameter plane analysis of a characteristic equation, which has not been analyzed in this way so far. We conclude with how quiescence of cells as well as two submodels for cell division may influence the possibility of destabilization via oscillations.

AB - © 2014 Society for Industrial and Applied Mathematics We propose a model to analyze the dynamics of interacting proliferating and quiescent cell populations. The model includes age dependence of cell division, transitions between the two subpopulations, and regulation of the recruitment of quiescent cells. We formulate the model as a pair of renewal equations and apply a rather recent general result to prove that (in)stability of equilibria can be analyzed by locating roots of characteristic equations. We are led to a parameter plane analysis of a characteristic equation, which has not been analyzed in this way so far. We conclude with how quiescence of cells as well as two submodels for cell division may influence the possibility of destabilization via oscillations.

KW - Age structure

KW - Cell population model

KW - Characteristic equation

KW - Hopf bifurcation

KW - Quiescence

KW - Renewal equation

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