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

Tomás Alarcón, Philipp Getto, Yukihiko Nakata

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    9 Citations (Scopus)


    © 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 languageEnglish
    Pages (from-to)1266-1297
    JournalSIAM Journal on Applied Mathematics
    Issue number4
    Publication statusPublished - 1 Jan 2014


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


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