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Influence of the age structure on the stability in a tumor-immune model for chronic myeloid leukemia

Kyriaki Dariva 1, 2 Thomas Lepoutre 2, 1
1 MMCS - Modélisation mathématique, calcul scientifique
ICJ - Institut Camille Jordan [Villeurbanne]
2 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
ICJ - Institut Camille Jordan [Villeurbanne], Inria Grenoble - Rhône-Alpes, CGPhiMC - Centre de génétique et de physiologie moléculaire et cellulaire
Abstract : We propose and analyze a system of partial differential equations (PDEs) for chronic myeloid leukemia (CML), generalizing the ordinary differential equations' system (ODE) proposed in [3, 2]. This model describes the proliferation and differentiation of leukemic cells in the bone marrow and the interactions of leukemic and immune cells. We consider that the differentiation of cells can be described by a continuous variable which we use to structure our system. The model is based on a non-monotonic immune response. At low levels, immune response increases with the tumor load whereas for high levels, tumor is suppressing the effect of immune system (immunosuppression). We analyze the stability of the steady states of the model and compare it to the case of [2] where maturity was described as a discrete state. In particular, a steady state describing remission induced by a control due to the immune system is shown to be unstable in certain situations for the PDE model , whereas in [2] it was systematically stable.
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Preprints, Working Papers, ...
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Contributor : Kyriaki Dariva Connect in order to contact the contributor
Submitted on : Tuesday, February 2, 2021 - 2:27:45 PM
Last modification on : Thursday, January 20, 2022 - 5:26:39 PM
Long-term archiving on: : Monday, May 3, 2021 - 8:01:00 PM


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  • HAL Id : hal-03128770, version 1


Kyriaki Dariva, Thomas Lepoutre. Influence of the age structure on the stability in a tumor-immune model for chronic myeloid leukemia. 2021. ⟨hal-03128770⟩



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