EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 15 (2020) Math. Model. Nat. Phenom., 15 (2020) 68 References
Open Access
Issue
Math. Model. Nat. Phenom.
Volume 15, 2020
Article Number 68
Number of page(s) 23
DOI https://doi.org/10.1051/mmnp/2020038
Published online 03 December 2020
  1. M. Adimy, A. Chekroun and C.P. Ferreira, Global dynamics of a differential-difference system: a case of Kermack-McKendrick SIR model with age-structured protection phase. Math. Biosci. Eng. 17 (2020) 1329–1354. [CrossRef] [Google Scholar]
  2. M. Adimy, A. Chekroun and T. Kuniya, Coupled reaction-diffusion and difference system of cell-cycle dynamics for hematopoiesis process with Dirichlet boundary conditions. J. Math. Anal. Appl. 479 (2019) 1030–1068. [CrossRef] [Google Scholar]
  3. M. Adimy, F. Crauste and S. Ruan, Periodic oscillations in leukopoiesis models with two delays. J. Theor. Biol. 242 (2006) 288–299. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  4. B. Ainseba and C. Benosman, Global dynamics of hematopoietic stem cells and differentiated cells in a chronic myeloid leukemia model. J. Math. Biol. 62 (2010) 975–997. [CrossRef] [PubMed] [Google Scholar]
  5. J.L. Avila, C. Bonnet, E. Fridman, F. Mazenc and J. Clairambault, Stability analysis of PDEs modelling cell dynamics in acute myeloid leukemia, in 53rd IEEE Conference on Decision and Control (2014). [Google Scholar]
  6. J.C. Banck and D. Gorlich, In-silico comparison of two induction regimens (7 + 3 vs 7 + 3 plus additional bone marrow evaluation) in acute myeloid leukemia treatment. BMC Syst. Biol. 13 (2019) 1–14. [CrossRef] [PubMed] [Google Scholar]
  7. E. Beretta and Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters. SIAM J. Math. Anal. 33 (2002) 1144–1165. [CrossRef] [MathSciNet] [Google Scholar]
  8. A. Besse, G.D. Clapp, S. Bernard, F.E. Nicolini, D. Levy and T. Lepoutre, Stability analysis of a model of interaction between the immune system and cancer cells in chronic myelogenous leukemia. Bull. Math. Biol. 80 (2017) 1084–1110. [CrossRef] [Google Scholar]
  9. A. Besse, T. Lepoutre and S. Bernard, Long-term treatment effects in chronic myeloid leukemia. J. Math. Biol. 75 (2017) 733–758. [CrossRef] [PubMed] [Google Scholar]
  10. M. Bouizem, B. Ainseba and A. Lakmeche, Mathematical analysis of an age structured leukemia model. Commun. Appl. Nonlinear Anal. 25 (2018) 1–20. [Google Scholar]
  11. N. Bouizem, M. Helal, N. Kherbouche and A. Lakmeche, Stability analysis of leukemia mathematical model with delay. Commun. Appl. Nonlinear Anal. 27 (2020) 25–57. [Google Scholar]
  12. F. Charif, M. Helal and A. Lakmeche, Chemotherapeutic treatment models by drugs with instantaneous effects. Commun. Appl. Nonlinear Anal. 24 (2017) 1–24. [Google Scholar]
  13. G.D. Clapp, T. Lepoutre, R.E. Cheikh, S. Bernard, J. Ruby, H. Labussiere-Wallet, F.E. Nicolini and D. Levy, Implication of the autologous immune system in BCR-ABL transcript variations in chronic myelogenous leukemia patients treated with imatinib. Cancer Res. 75 (2015) 4053–4062. [CrossRef] [Google Scholar]
  14. C. Colijn and M. Mackey, A mathematical model of hematopoiesis: II. cyclical neutropenia. J. Theor. Biol. 237 (2005) 133–146. [CrossRef] [PubMed] [Google Scholar]
  15. A.S. Corbin, A. Agarwal, M. Loriaux, J. Cortes, M.W. Deininger and B.J. Druker, Human chronic myeloid leukemia stem cells are insensitive to imatinib despite inhibition of BCR-ABL activity. J. Clin. Invest. 121 (2011) 396–409. [CrossRef] [PubMed] [Google Scholar]
  16. D. Dingli and F. Michor, Successful therapy must eradicate cancer stem cells. Stem Cells 24 (2006) 2603–2610. [CrossRef] [PubMed] [Google Scholar]
  17. D. Dingli, A. Traulsen and J.M. Pacheco, Stochastic dynamics of hematopoietic tumor stem cells. Cell Cycle 6 (2007) 461–466. [CrossRef] [PubMed] [Google Scholar]
  18. J. Foo, M.W. Drummond, B. Clarkson, T. Holyoake and F. Michor, Eradication of chronic Myeloid Leukemia stem cells: a novel mathematical model predicts no therapeutic benefit of adding G-CSF to Imatinib. PLOS Comput. Biol. 5 (2009) e1000503. [CrossRef] [Google Scholar]
  19. H.I. Freedman and P. Moson, Persistence definitions and their connections. Proc. Am. Math. Soc. 109 (1990) 1025–1033. [CrossRef] [Google Scholar]
  20. J.K. Hale and S.M. Verduyn Lunel, Introduction to Functional Differential Equations. Springer (1993). [Google Scholar]
  21. Y. Isma, M. Helal and A. Lakmeche, Existence and stability of steady states for a delay model of stem cells in leukemia under treatment. Commun. Appl. Nonlinear Anal. 25 (2018) 66–80. [Google Scholar]
  22. C.H. Jerome Paillassa, KB / iKB Hematologie Onco-hematologie. Masson (2018). [Google Scholar]
  23. X. Jiang, Y. Zhao, C. Smith, M. Gasparetto, A. Turhan, A. Eaves and C. Eaves, Chronic myeloid leukemia stem cells possess multiple unique features of resistance to BCR-ABL targeted therapies. Leukemia 21 (2007) 926–935. [CrossRef] [PubMed] [Google Scholar]
  24. H.G. Jorgensen, E.K. Allan, N.E. Jordanides, J.C. Mountford and T.L. Holyoake, Nilotinib exerts equipotent antiproliferative effects to imatinib and does not induce apoptosis in CD34+ CML cells. Blood 109 (2007) 4016–4019. [CrossRef] [Google Scholar]
  25. F. Jost, E. Schalk, K. Rinke, T. Fischer and S. Sager, Mathematical models for cytarabine-derived myelosuppression in acute myeloid leukaemia. PLOS ONE 14 (2019) e0204540. [CrossRef] [Google Scholar]
  26. P.S. Kim, P.P. Lee and D. Levy, A PDE model for imatinib-treated chronic myelogenous leukemia. Bull. Math. Biol. 70 (2008) 1994–2016. [CrossRef] [Google Scholar]
  27. F. Knauer, T. Stiehl and A. Marciniak-Czochra, Oscillations in a white blood cell production model with multiple differentiation stages. J. Math. Biol. 80 (2019) 575–600. [CrossRef] [PubMed] [Google Scholar]
  28. Y. Kuang, Delay Differential Equations: With Applications in Population Dynamics. Academic Press (1993). [Google Scholar]
  29. U. Ledzewicz and H. Moore, Dynamical systems properties of a mathematical model for the treatment of CML. Appl. Sci. 6 (2016) 291. [CrossRef] [Google Scholar]
  30. T. Lorenzi, A. Marciniak-Czochra and T. Stiehl, A structured population model of clonal selection in acute leukemias with multiple maturation stages. J. Math. Biol. 79 (2019) 1587–1621. [CrossRef] [PubMed] [Google Scholar]
  31. M.C. Mackey, Unified hypothesis for the origin of aplastic anemia and periodic hematopoiesis. Blood 51 (1978) 941–956. [PubMed] [Google Scholar]
  32. F. Michor, Quantitative approaches to analyzing imatinib-treated chronic myeloid leukemia. TRENDS in Pharmacolog. Sci. 28 (2007) 197–198. [CrossRef] [Google Scholar]
  33. F. Michor. Reply: The long-term response to imatinib treatment of CML. Br. J. Cancer 96 (2007) 679–680. [CrossRef] [Google Scholar]
  34. F. Michor, Chronic Myeloid Leukemia Blast Crisis Arises from Progenitors. Stem Cells 25 (2007) 1114–1118. [CrossRef] [PubMed] [Google Scholar]
  35. F. Michor, T.P. Hughes, Y. Iwasa, S. Branford, N.P. Shah, C.L. Sawyers and M.A. Nowak, Dynamics of chronic myeloid leukaemia. Nature 435 (2005) 1267–1270. [CrossRef] [PubMed] [Google Scholar]
  36. S. Mustjoki, J. Richter, G. Barbany, H. Ehrencrona, T. Fioretos, T. Gedde-Dahl, B.T. Gjertsen, R. Hovland, S. Hernesniemi, D. Josefsen, P. Koskenvesa, I. Dybedal, B. Markevärn, T. Olofsson, U. Olsson-Strömberg, K. Rapakko, S. Thunberg, L. Stenke, B. Simonsson, K. Porkka and H. Hjorth-Hansen, Nordic CML Study Group (NCMLSG). Impact of malignant stem cell burden on therapy outcome in newly diagnosed chronic myeloid leukemia patients. Leukemia 27 (2013) 1520–1526. [CrossRef] [PubMed] [Google Scholar]
  37. S. Nanda, H. Moore and S. Lenhart, Optimal control of treatment in a mathematical model of chronic myelogenous leukemia. Math. Biosci. 210 (2007) 143–156. [CrossRef] [Google Scholar]
  38. H.G. Othmer, F. Adler, M. Lewis and J. Dallon, Case Studies in Mathematical Modeling: Ecology, Physiology, and Cell Biology. Pearson (1997). [Google Scholar]
  39. L. Pujo-Menjouet, S. Bernard and M.C. Mackey, Long period oscillations in a G0 model of hematopoietic stem cells. SIAM J. Appl. Dyn. Syst. 4 (2005) 312–332. [CrossRef] [Google Scholar]
  40. I.R. Radulescu, D. Cândea and A. Halanay, Optimal control analysis of a leukemia model under imatinib treatment. Math. Comput. Simul. 121 (2016) 1–11. [CrossRef] [Google Scholar]
  41. I.R. Radulescu, D. Cândea and A. Halanay, Stability and bifurcation in a model for the dynamics of stem-like cells in leukemia under treatment. AIP Conf. Proc. 1493 (2012) 758. [CrossRef] [Google Scholar]
  42. I. Roeder, M. Herberg and M. Horn, An age structured model of hematopoietic stem cell organization with application to chronic myeloid leukemia. Bull. Math. Biol. 71 (2008) 602–626. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  43. I. Roeder, M. Horn, I. Glauche, A. Hochhaus, M.C. Mueller and M. Loeffler, Dynamic modeling of imatinib-treated chronic myeloid leukemia: functional insights and clinical implications. Nat. Med. 12 (2006) 1181–1184. [CrossRef] [PubMed] [Google Scholar]
  44. J.A. Sharp, A.P. Browning, T. Mapder, K. Burrage and M.J. Simpson, Optimal control of acute myeloid leukaemia. J. Theor. Biol. 470 (2019) 30–42. [CrossRef] [PubMed] [Google Scholar]
  45. H. Smith, An Introduction to Delay Differential Equations with Applications to the Life Sciences. Texts in Applied Mathematics. Springer (2011). [CrossRef] [Google Scholar]
  46. T. Stiehl, N. Baran, A.D. Ho and A. Marciniak-Czochra, Clonal selection and therapy resistance in acute leukaemias: mathematical modelling explains different proliferation patterns at diagnosis and relapse. J. Roy. Soc. Interface 11 (2014) 20140079. [CrossRef] [Google Scholar]
  47. T. Stiehl, C. Lutz and A. Marciniak-Czochra, Emergence of heterogeneity in acute leukemias. Biol. Direct 11 (2016). [CrossRef] [Google Scholar]
  48. T. Stiehl and A. Marciniak-Czochra, Mathematical modelling of leukemogenesis and cancer stem celldynamics. MMNP 7 (2012) 166–202. [CrossRef] [EDP Sciences] [Google Scholar]
  49. M. Tang, J. Foo, M. Gonen, J. Guilhot, F.X. Mahon and F. Michor, Selection pressure exerted by imatinib therapy leads to disparate outcomes of imatinib discontinuation trials. Haematologica 97 (2012) 1553–1561. [CrossRef] [PubMed] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.