{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T08:32:30Z","timestamp":1793521950365,"version":"4.5.0"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2010,1,14]],"date-time":"2010-01-14T00:00:00Z","timestamp":1263427200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. Math. Biol."],"published-print":{"date-parts":[[2010,10]]},"DOI":"10.1007\/s11538-009-9500-0","type":"journal-article","created":{"date-parts":[[2010,1,13]],"date-time":"2010-01-13T17:03:25Z","timestamp":1263402205000},"page":"1732-1759","source":"Crossref","is-referenced-by-count":25,"title":["Stability Analysis of a Simplified Yet Complete Model for\u00a0Chronic Myelogenous Leukemia"],"prefix":"10.1007","volume":"72","author":[{"given":"Marie","family":"Doumic-Jauffret","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter S.","family":"Kim","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Beno\u00eet","family":"Perthame","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2010,1,14]]},"reference":[{"issue":"4","key":"9500_CR1","doi-asserted-by":"crossref","first-page":"1328","DOI":"10.1137\/040604698","volume":"65","author":"M. Adimy","year":"2005","unstructured":"Adimy, M., Crauste, F., Ruan, S., 2005. A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia. SIAM J. Appl. Math. 65(4), 1328\u20131352.","journal-title":"SIAM J. Appl. Math."},{"issue":"3","key":"9500_CR2","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1142\/S0218339008002599","volume":"16","author":"M. Adimy","year":"2008","unstructured":"Adimy, M., Crauste, F., El Abdllaoui, A., 2008. Discrete maturity-structured model of cell differentiation with applications to acute myelogenous leukemia. J. Biol. Syst. 16(3), 395\u2013424.","journal-title":"J. Biol. Syst."},{"key":"9500_CR3","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.cell.2004.07.004","volume":"118","author":"F. Arai","year":"2004","unstructured":"Arai, F., Hirao, A., Ohmura, M., Sato, H., Matsuoka, S., Takubo, K., Ito, K., Koh, G.Y., Suda, T., 2004. Tie2\/angiopoietin-1 signaling regulates hematopoietic stem cell quiescence in the bone marrow niche. Cell 118, 149\u2013161.","journal-title":"Cell"},{"issue":"3","key":"9500_CR4","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/S0022-5193(03)00090-0","volume":"223","author":"S. Bernard","year":"2003","unstructured":"Bernard, S., B\u00e9lair, J., Mackey, M.C., 2003. Oscillations in cyclical neutropenia: new evidence based on mathematical modeling. J. Theor. Biol. 223(3), 283\u2013298.","journal-title":"J. Theor. Biol."},{"issue":"3","key":"9500_CR5","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/j.crvi.2003.05.005","volume":"227","author":"S. Bernard","year":"2004","unstructured":"Bernard, S., B\u00e9lair, J., Mackey, M.C., 2004. Bifurcations in a white-blood cell production model. C. R. Biol. 227(3), 201\u2013210.","journal-title":"C. R. Biol."},{"issue":"7","key":"9500_CR6","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1038\/nm0797-730","volume":"3","author":"D. Bonnet","year":"1997","unstructured":"Bonnet, D., Dick, J.E., 1997. Human acute myeloid leukemia is organized as a hierarchy that originates from a primitive hematopoietic cell. Nat. Med. 3(7), 730\u2013737.","journal-title":"Nat. Med."},{"issue":"5","key":"9500_CR7","first-page":"445","volume":"25","author":"G.B. Bradford","year":"1997","unstructured":"Bradford, G.B., Williams, B., Rossi, R., Bertoncello, I., 1997. Quiescence, cycling, and turnover in the primitive hematopoietic stem cell compartment. Exp. Hematol. 25(5), 445\u2013453.","journal-title":"Exp. Hematol."},{"issue":"7\u20138","key":"9500_CR8","first-page":"699","volume":"47","author":"F.B. Brikci","year":"2007","unstructured":"Brikci, F.B., Clairambault, J., Perthame, B., 2007. Analysis of a molecular structured population model with possible polynomial growth for the cell division cycle. Math. Methods Model. Biophys. Phenom. 47(7\u20138), 699\u2013713. Special Issue of Mathematical and Computer Modelling.","journal-title":"Math. Methods Model. Biophys. Phenom."},{"issue":"1","key":"9500_CR9","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/s00285-007-0147-x","volume":"57","author":"F.B. Brikci","year":"2008","unstructured":"Brikci, F.B., Clairambault, J., Perthame, B., Ribba, B., 2008. An age-and-cyclin structured cell population model for healthy and tumoral tissues. J. Math. Biol. 57(1), 91\u2013110.","journal-title":"J. Math. Biol."},{"issue":"1","key":"9500_CR10","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1080\/17513750902935208","volume":"4","author":"V. Calvez","year":"2010","unstructured":"Calvez, V., Lenuzza, N., Doumic, M., Deslys, J.-P., Mouthon, F., Perthame, B., 2010. Prion dynamic with size dependency-strain phenomena. J. Biol. Dyn. 4(1), 28\u201342.","journal-title":"J. Biol. Dyn."},{"key":"9500_CR11","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.mbs.2008.10.007","volume":"217","author":"V. Calvez","year":"2009","unstructured":"Calvez, V., Lenuzza, N., Oelz, D., Deslys, J.-P., Laurent, P., Mouthon, F., Perthame, B., 2009. Size distribution dependence of prion aggregates infectivity. Math. Biosci. 217, 88\u201399.","journal-title":"Math. Biosci."},{"issue":"6","key":"9500_CR12","doi-asserted-by":"crossref","first-page":"3120","DOI":"10.1073\/pnas.96.6.3120","volume":"96","author":"S.H. Cheshier","year":"1999","unstructured":"Cheshier, S.H., Morrison, S.J., Liao, X., Weissman, I.L., 1999. In vivo proliferation and cell cycle kinetics of long-term self-renewing. Proc. Natl. Acad. Sci. USA 96(6), 3120\u20133125.","journal-title":"Proc. Natl. Acad. Sci. USA"},{"issue":"2","key":"9500_CR13","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.jtbi.2005.03.033","volume":"237","author":"C. Colijn","year":"2005","unstructured":"Colijn, C., Mackey, M.C., 2005a. A mathematical model of hematopoiesis\u2014I. Periodic chronic myelogenous leukemia. J. Theor. Biol. 237(2), 117\u2013132.","journal-title":"J. Theor. Biol."},{"issue":"2","key":"9500_CR14","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.jtbi.2005.03.034","volume":"237","author":"C. Colijn","year":"2005","unstructured":"Colijn, C., Mackey, M.C., 2005b. A mathematical model of hematopoiesis\u2014II. Cyclical neutropenia. J.\u00a0Theor. Biol. 237(2), 133\u2013146.","journal-title":"J.\u00a0Theor. Biol."},{"issue":"1","key":"9500_CR15","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.jtbi.2005.02.015","volume":"236","author":"R. DeConde","year":"2005","unstructured":"DeConde, R., Kim, P.S., Levy, D., Lee, P.P., 2005. Post-transplantation dynamics of the immune response to chronic myelogenous leukemia. J. Theor. Biol. 236(1), 39\u201359.","journal-title":"J. Theor. Biol."},{"key":"9500_CR16","series-title":"Appl. Math. Sciences","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4206-2","volume-title":"Delay Equations, Functional, Complex and Nonlinear Analysis","author":"O. Diekmann","year":"1995","unstructured":"Diekmann, O., van Gils, S.A., Verduyn-Lunel, S.M., Walther, H.-O., 1995. Delay Equations, Functional, Complex and Nonlinear Analysis. Appl. Math. Sciences, vol.\u00a0110. Springer, New York."},{"issue":"3","key":"9500_CR17","first-page":"121","volume":"2","author":"M. Doumic","year":"2007","unstructured":"Doumic, M., 2007. Analysis of a population model structured by the cells molecular content. Math. Methods Model. Biophys. Phenom. 2(3), 121\u2013152.","journal-title":"Math. Methods Model. Biophys. Phenom."},{"key":"9500_CR18","doi-asserted-by":"crossref","unstructured":"Doumic, M., Perthame, B., Zubelli, J.P., 2009. Numerical solution of an inverse problem in size-structured population dynamics. Inverse Probl. 25.","DOI":"10.1088\/0266-5611\/25\/4\/045008"},{"issue":"1","key":"9500_CR19","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1172\/JCI9083","volume":"105","author":"B.J. Druker","year":"2000","unstructured":"Druker, B.J., Lydon, N.B., 2000. Lessons learned from the development of an ABL tyrosine kinase inhibitor for chronic myelogenous leukemia. J. Clin. Invest. 105(1), 3\u20137.","journal-title":"J. Clin. Invest."},{"key":"9500_CR20","unstructured":"Engelborghs, K., Luzyanina, T., Samaey, G., 2001. DDE-BIFTOOL v. 2.00: A Matlab package for bifurcation analysis of delay differential equations. http:\/\/twr.cs.kuleuven.be\/research\/software\/delay\/ddebiftool.shtml ."},{"issue":"8","key":"9500_CR21","first-page":"2084","volume":"51","author":"A.S. Fokas","year":"1991","unstructured":"Fokas, A.S., Keller, J.B., Clarkson, B.D., 1991. Mathematical model of granulocytopoiesis and chronic myelogenous leukemia. Cancer Res. 51(8), 2084\u20132091.","journal-title":"Cancer Res."},{"key":"9500_CR22","doi-asserted-by":"crossref","first-page":"1109","DOI":"10.1016\/j.cell.2005.05.026","volume":"121","author":"M.J. Kiel","year":"2005","unstructured":"Kiel, M.J., Yilmaz, O.H., Iwashita, T., Yilmaz, O.H., Terhorst, C., Morrison, S.J., 2005. SLAM family receptors distinguish hematopoietic stem and progenitor cells and reveal endothelial niches for stem cells. Cell 121, 1109\u20131121.","journal-title":"Cell"},{"issue":"1","key":"9500_CR23","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.jtbi.2006.12.012","volume":"246","author":"P.S. Kim","year":"2007","unstructured":"Kim, P.S., Lee, P.P., Levy, D., 2007. Modeling regulation mechanisms of the immune system. J. Theor. Biol. 246(1), 33\u201369.","journal-title":"J. Theor. Biol."},{"issue":"6","key":"9500_CR24","volume":"4","author":"P.S. Kim","year":"2008","unstructured":"Kim, P.S., Lee, P.P., Levy, D., 2008a. Dynamics and potential impact of the immune response to chronic myelogenous leukemia. PLoS Comput. Biol. 4(6), e1000095.","journal-title":"PLoS Comput. Biol."},{"issue":"3","key":"9500_CR25","doi-asserted-by":"crossref","first-page":"728","DOI":"10.1007\/s11538-007-9276-z","volume":"70","author":"P.S. Kim","year":"2008","unstructured":"Kim, P.S., Lee, P.P., Levy, D., 2008b. Modeling imatinib-treated chronic myelogenous leukemia: reducing the complexity of agent-based models. Bull. Math. Biol. 70(3), 728\u2013744.","journal-title":"Bull. Math. Biol."},{"issue":"7","key":"9500_CR26","first-page":"1994\u20132016","volume":"70","author":"P.S. Kim","year":"2008","unstructured":"Kim, P.S., Lee, P.P., Levy, D., 2008c. A PDE model for imatinib-treated chronic myelogenous leukemia. Bull. Math. Biol. 70(7), 1994\u20132016.","journal-title":"Bull. Math. Biol."},{"issue":"27","key":"9500_CR27","doi-asserted-by":"crossref","first-page":"9714","DOI":"10.1073\/pnas.0501870102","volume":"102","author":"N.L. Komarova","year":"2005","unstructured":"Komarova, N.L., Wodarz, D., 2005. Drug resistance in cancer: principles of emergence and prevention. Proc. Natl. Acad. Sci. USA 102(27), 9714\u20139719.","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"9500_CR28","doi-asserted-by":"crossref","unstructured":"Magal, P., Ruan, S., 2009. Center manifolds for semilinear equations with non-dense domain and applications on Hopf bifurcation in age structured models. Mem. Am. Math. Soc. 202(951).","DOI":"10.1090\/S0065-9266-09-00568-7"},{"key":"9500_CR29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1089\/scd.2008.0013","volume":"17","author":"A. Marciniak","year":"2008","unstructured":"Marciniak, A., Stiehl, T., Ho, A.D., Jaeger, W., Wagner, W., 2008. Modeling asymmetric cell division in hematopietic stem cells\u2014regulation of self-renewal is essential for efficient repopulation. Stem Cells Dev. 17, 1\u201310.","journal-title":"Stem Cells Dev."},{"key":"9500_CR30","doi-asserted-by":"crossref","first-page":"1235","DOI":"10.1016\/j.matpur.2005.04.001","volume":"84","author":"P. Michel","year":"2005","unstructured":"Michel, P., Mischler, S., Perthame, B., 2005. General relative entropy inequality: an illustration on growth models. J. Math. Pures Appl. 84, 1235\u20131260.","journal-title":"J. Math. Pures Appl."},{"issue":"17","key":"9500_CR31","doi-asserted-by":"crossref","first-page":"2854","DOI":"10.1200\/JCO.2007.15.2421","volume":"26","author":"F. Michor","year":"2008","unstructured":"Michor, F., 2008. Mathematical models of cancer stem cells. J. Clin. Oncol. 26(17), 2854\u20132861.","journal-title":"J. Clin. Oncol."},{"issue":"7046","key":"9500_CR32","doi-asserted-by":"crossref","first-page":"1267","DOI":"10.1038\/nature03669","volume":"435","author":"F. Michor","year":"2005","unstructured":"Michor, F., Hughes, T.P., Iwasa, Y., Branford, S., Shah, N.P., Sawyers, C.L., Nowak, M.A., 2005. Dynamics of chronic myeloid leukemia. Nature 435(7046), 1267\u20131270.","journal-title":"Nature"},{"issue":"4","key":"9500_CR33","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1016\/j.jtbi.2003.11.024","volume":"225","author":"H. Moore","year":"2004","unstructured":"Moore, H., Li, N.K., 2004. A mathematical model for chronic myelogenous leukemia (CML) and T cell interaction. J. Theor. Biol. 225(4), 513\u2013523.","journal-title":"J. Theor. Biol."},{"key":"9500_CR34","unstructured":"Neiman, B., 2002. A mathematical model of chronic myelogenous leukemia. Master\u2019s thesis, University College, Oxford University, Oxford, UK."},{"key":"9500_CR35","volume-title":"Frontiers in Mathematics","author":"B. Perthame","year":"2007","unstructured":"Perthame, B., 2007. Transport equations arising in biology. In: Frontiers in Mathematics, Birkhauser, Boston."},{"issue":"3","key":"9500_CR36","doi-asserted-by":"crossref","first-page":"1037","DOI":"10.1088\/0266-5611\/23\/3\/012","volume":"23","author":"B. Perthame","year":"2007","unstructured":"Perthame, B., Zubelli, J.P., 2007. On the inverse problem for a size-structured population model. Inverse Probl. 23(3), 1037\u20131052.","journal-title":"Inverse Probl."},{"key":"9500_CR37","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.crvi.2003.05.004","volume":"327","author":"L. Pujo-Menjouet","year":"2004","unstructured":"Pujo-Menjouet, L., Mackey, M.C., 2004. Contribution to the study of periodic chronic myelogenous leukemia. C. R. Biol. 327, 235\u2013244.","journal-title":"C. R. Biol."},{"key":"9500_CR38","unstructured":"Roeder, I., 2005. Dynamic modeling of hematopoietic stem cell organization\u2014design and validation of the new concept of within-tissue plasticity. PhD thesis, University of Leipzig, Leipzig, Germany."},{"issue":"10","key":"9500_CR39","doi-asserted-by":"crossref","first-page":"1181","DOI":"10.1038\/nm1487","volume":"12","author":"I. Roeder","year":"2006","unstructured":"Roeder, I., Horn, M., Glauche, I., Hochhaus, A., Mueller, M.C., Loeffler, M., 2006. Dynamic modeling of imatinib-treated chronic myeloid leukemia: functional insights and clinical implications. Nat. Med. 12(10), 1181\u20131184.","journal-title":"Nat. Med."},{"issue":"3","key":"9500_CR40","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1007\/s11538-008-9373-7","volume":"71","author":"I. Roeder","year":"2009","unstructured":"Roeder, I., Herberg, M., Horn, M., 2009. An \u201cage\u201d-structured model of hematopoietic stem cell organization with application to chronic myeloid leukemia. Bull. Math. Biol. 71(3), 602\u2013626.","journal-title":"Bull. Math. Biol."},{"key":"9500_CR41","doi-asserted-by":"crossref","first-page":"2631","DOI":"10.1182\/blood-2004-06-2480","volume":"105","author":"R.S. Taichman","year":"2005","unstructured":"Taichman, R.S., 2005. Blood and bone: two tissues whose fates are intertwined to create the hematopoietic stem-cell niche. Blood 105, 2631\u20132639.","journal-title":"Blood"},{"issue":"11","key":"9500_CR42","doi-asserted-by":"crossref","first-page":"1646","DOI":"10.1038\/sj.leu.2401565","volume":"13","author":"S.F.T. Thijsen","year":"1999","unstructured":"Thijsen, S.F.T., Schuurhuis, G.J., van Oostveen, J.W., Ossenkoppele, G.J., 1999. Chronic mlyeloid leukemia from basics to bedside. Leukemia 13(11), 1646\u20131674.","journal-title":"Leukemia"},{"key":"9500_CR43","doi-asserted-by":"crossref","first-page":"1427","DOI":"10.1126\/science.287.5457.1427","volume":"287","author":"F.M. Watt","year":"2000","unstructured":"Watt, F.M., Hogan, B.L., 2000. Out of Eden: stem cells and their niches. Science 287, 1427\u20131430.","journal-title":"Science"}],"container-title":["Bulletin of Mathematical Biology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11538-009-9500-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11538-009-9500-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11538-009-9500-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,3]],"date-time":"2019-06-03T11:00:10Z","timestamp":1559559610000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11538-009-9500-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1,14]]},"references-count":43,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2010,10]]}},"alternative-id":["9500"],"URL":"https:\/\/doi.org\/10.1007\/s11538-009-9500-0","relation":{},"ISSN":["0092-8240","1522-9602"],"issn-type":[{"value":"0092-8240","type":"print"},{"value":"1522-9602","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1,14]]}}}