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A model for megakaryopoiesis with state-dependent delay

Abstract : We analyze the stability of a system of differential equations with a threshold-defined delay arising from a model for platelet production. We consider a maturity-structured population of megakaryocyte progenitors and an age-structured population of platelets, where the cytokine thrombopoietin (TPO) increases the maturation rate of progenitors. Using the quasi-steady-state approximation for TPO dynamics and the method of characteristics, partial differential equations are reduced to a system of two differential equations with a state-dependent delay accounting for the variable maturation rate. We start by introducing the model and proving the positivity and boundedness of the solutions. Then we use a change of variables to obtain an equivalent system of two differential equations with a constant delay, from which we prove existence and uniqueness of the solution. As linearization around the unique positive steady state yields a transcendental characteristic equation of third degree, we introduce the main result, a new framework for stability analysis on models with fixed delays. This framework is then used to describe the stability of the megakaryopoiesis with respect to its parameters. Finally, with parameters being obtained and estimated from data, we give an example in which oscillations appear when the death rate of progenitors is increased 10-fold.
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https://hal.inria.fr/hal-02123621
Contributor : Loïs Boullu <>
Submitted on : Wednesday, May 8, 2019 - 4:06:49 PM
Last modification on : Monday, June 28, 2021 - 2:26:03 PM
Long-term archiving on: : Friday, August 9, 2019 - 12:16:09 PM

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Loïs Boullu, Laurent Pujo-Menjouet, Jianhong Wu. A model for megakaryopoiesis with state-dependent delay. SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2019, 79 (4), pp.1218-1243. ⟨10.1137/18M1201020⟩. ⟨hal-02123621⟩

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