Stability Analysis of a Model of Interaction Between the Immune System and Cancer Cells in Chronic Myelogenous Leukemia

  • Apollos Besse
  • Geoffrey D. Clapp
  • Samuel Bernard
  • Franck E. Nicolini
  • Doron Levy
  • Thomas Lepoutre
Special Issue : Mathematical Oncology


We describe here a simple model for the interaction between leukemic cells and the autologous immune response in chronic phase chronic myelogenous leukemia (CML). This model is a simplified version of the model we proposed in Clapp et al. (Cancer Res 75:4053–4062, 2015). Our simplification is based on the observation that certain key characteristics of the dynamics of CML can be captured with a three-compartment model: two for the leukemic cells (stem cells and mature cells) and one for the immune response. We characterize the existence of steady states and their stability for generic forms of immunosuppressive effects of leukemic cells. We provide a complete co-dimension one bifurcation analysis. Our results show how clinical response to tyrosine kinase inhibitors treatment is compatible with the existence of a stable low disease, treatment-free steady state.


Chronic myelogenous leukemia Immune response Bifurcation analysis Linear stability 



The work of GC was supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE1322106. The work of DL was supported in part by the John Simon Guggenheim Memorial Foundation. The work was supported by the Inria Partnerships Program grant “Modelling Leukemia.”


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Copyright information

© Society for Mathematical Biology 2017

Authors and Affiliations

  1. 1.Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208Institut Camille JordanVilleurbanne cedexFrance
  2. 2.INRIAVilleurbanneFrance
  3. 3.Department of MathematicsUniversity of MarylandCollege ParkUSA
  4. 4.Hematology Department 1GCentre Hospitalier Lyon SudPierre BéniteFrance
  5. 5.INSERM U1052 Centre de Recherche en Cancérologie de LyonLyonFrance
  6. 6.Department of Mathematics and Center for Scientific Computation and Mathematical Modeling (CSCAMM)University of MarylandCollege ParkUSA

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