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Age-structured and delay differential-difference model of hematopoietic stem cell dynamics
1. | Inria, Université de Lyon, Université Lyon 1, Institut Camille Jordan, 43 Bd. du 11 novembre 1918, F-69200 Villeurbanne Cedex, France, France |
2. | Department of Mathematics, University Aboubekr Belkaid, Tlemcen, Algeria |
References:
[1] |
M. Adimy, O. Angulo, C. Marquet and L. Sebaa, A mathematical model of multistage hematopoietic cell lineages, Discrete and Continuous Dynamical Systems - Series B, 19 (2014), 1-26.
doi: 10.3934/dcdsb.2014.19.1. |
[2] |
M. Adimy and F. Crauste, Global stability of a partial differential equation with distributed delay due to cellular replication, Nonlinear Analysis: Theory, Methods & Applications, 54 (2003), 1469-1491.
doi: 10.1016/S0362-546X(03)00197-4. |
[3] |
M. Adimy and F. Crauste, Modeling and asymptotic stability of a growth factor-dependent stem cell dynamics model with distributed delay, Discrete and Continuous Dynamical Systems - Series B, 8 (2007), 19-38.
doi: 10.3934/dcdsb.2007.8.19. |
[4] |
M. Adimy, F. Crauste, H. Hbid and R. Qesmi, Stability and Hopf bifurcation for a cell population model with state-dependent delay, SIAM Journal on Applied Mathematics, 70 (2010), 1611-1633.
doi: 10.1137/080742713. |
[5] |
M. Adimy, F. Crauste and S. Ruan, A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia, SIAM Journal on Applied Mathematics, 65 (2005), 1328-1352.
doi: 10.1137/040604698. |
[6] |
J. Bélair, M. C. Mackey and J. M. Mahaffy, Age-structured and two-delay models for erythropoiesis, Math Biosci, 128 (1995), 317-346, URL http://www.sciencedirect.com/science/article/pii/002555649400078E. |
[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.
doi: 10.1137/S0036141000376086. |
[8] |
S. Bernard, J. Bélair and M. C. Mackey, Oscillations in cyclical neutropenia: New evidence based on mathematical modeling, Journal of Theoretical Biology, 223 (2003), 283-298, URL http://www.ams.org/mathscinet-getitem?mr=2079467.
doi: 10.1016/S0022-5193(03)00090-0. |
[9] |
S. Bernard, J. Bélair and M. C. Mackey, Bifurcations in a white-blood-cell production model, C. R. Biol., 327 (2004), 201-210, URL http://linkinghub.elsevier.com/retrieve/pii/S1631069104000381.
doi: 10.1016/j.crvi.2003.05.005. |
[10] |
F. J. Burns and I. F. Tannock, On the existence of a G$_0$-phase in the cell cycle, Cell Proliferation, 3 (1970), 321-334.
doi: 10.1111/j.1365-2184.1970.tb00340.x. |
[11] |
C. Colijn and M. C. Mackey, A mathematical model of hematopoiesis - I. Periodic chronic myelogenous leukemia, Journal of Theoretical Biology, 237 (2005), 117-132.
doi: 10.1016/j.jtbi.2005.03.033. |
[12] |
F. Ficara, M. J. Murphy, M. Lin and M. L. Cleary, Pbx1 regulates self-renewal of long-term hematopoietic stem cells by maintaining their quiescence, Cell Stem Cell, 2 (2008), 484-496, URL http://www.sciencedirect.com/science/article/pii/S1934590908001161.
doi: 10.1016/j.stem.2008.03.004. |
[13] |
K. Gu and Y. Liu, Lyapunov-Krasovskii functional for uniform stability of coupled differential-functional equations, Automatica, 45 (2009), 798-804.
doi: 10.1016/j.automatica.2008.10.024. |
[14] |
J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer New York, 1993.
doi: 10.1007/978-1-4612-4342-7. |
[15] |
Y. Kuang, Delay Differential Equations: With Applications in Population Dynamics, Academic Press, San Diego, 1993. |
[16] |
J. Lei and M. C. Mackey, Multistability in an age-structured model of hematopoiesis: Cyclical neutropenia, Journal of Theoretical Biology, 270 (2011), 143-153.
doi: 10.1016/j.jtbi.2010.11.024. |
[17] |
M. C. Mackey, Unified hypothesis for the origin of aplastic anemia and periodic hematopoiesis., Blood, 51 (1978), 941-956. |
[18] |
L. Pujo-Menjouet, S. Bernard and M. C. Mackey, Long period oscillations in a $G_0$ model of hematopoietic stem cells, SIAM J. Appl. Dyn. Syst., 4 (2005), 312-332.
doi: 10.1137/030600473. |
[19] |
L. Pujo-Menjouet and M. C. Mackey, Contribution to the study of periodic chronic myelogenous leukemia, C. R. Biol., 327 (2004), 235-244, URL http://linkinghub.elsevier.com/retrieve/pii/S1631069104000253.
doi: 10.1016/j.crvi.2003.05.004. |
[20] |
H. Takizawa, R. R. Regoes, C. S. Boddupalli, S. Bonhoeffer and M. G. Manz, Dynamic variation in cycling of hematopoietic stem cells in steady state and inflammation, J. Exp. Med., 208 (2011), 273-284, URL http://jem.rupress.org/content/208/2/273.full. |
[21] |
P. Vegh, J. Winckler and F. Melchers, Long-term "in vitro'' proliferating mouse hematopoietic progenitor cell lines, Immunology Letters, 130 (2010), 32-35, URL http://www.sciencedirect.com/science/article/pii/S0165247810000544.
doi: 10.1016/j.imlet.2010.02.001. |
[22] |
A. Wilson, E. Laurenti, G. Oser, R. C. van der Wath, W. Blanco-Bose, M. Jaworski, S. Offner, C. F. Dunant, L. Eshkind, E. Bockamp, P. Lió, H. R. MacDonald and A. Trumpp, Hematopoietic stem cells reversibly switch from dormancy to self-renewal during homeostasis and repair, Cell, 135 (2008), 1118-1129, URL http://www.sciencedirect.com/science/article/pii/S009286740801386X. |
show all references
References:
[1] |
M. Adimy, O. Angulo, C. Marquet and L. Sebaa, A mathematical model of multistage hematopoietic cell lineages, Discrete and Continuous Dynamical Systems - Series B, 19 (2014), 1-26.
doi: 10.3934/dcdsb.2014.19.1. |
[2] |
M. Adimy and F. Crauste, Global stability of a partial differential equation with distributed delay due to cellular replication, Nonlinear Analysis: Theory, Methods & Applications, 54 (2003), 1469-1491.
doi: 10.1016/S0362-546X(03)00197-4. |
[3] |
M. Adimy and F. Crauste, Modeling and asymptotic stability of a growth factor-dependent stem cell dynamics model with distributed delay, Discrete and Continuous Dynamical Systems - Series B, 8 (2007), 19-38.
doi: 10.3934/dcdsb.2007.8.19. |
[4] |
M. Adimy, F. Crauste, H. Hbid and R. Qesmi, Stability and Hopf bifurcation for a cell population model with state-dependent delay, SIAM Journal on Applied Mathematics, 70 (2010), 1611-1633.
doi: 10.1137/080742713. |
[5] |
M. Adimy, F. Crauste and S. Ruan, A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia, SIAM Journal on Applied Mathematics, 65 (2005), 1328-1352.
doi: 10.1137/040604698. |
[6] |
J. Bélair, M. C. Mackey and J. M. Mahaffy, Age-structured and two-delay models for erythropoiesis, Math Biosci, 128 (1995), 317-346, URL http://www.sciencedirect.com/science/article/pii/002555649400078E. |
[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.
doi: 10.1137/S0036141000376086. |
[8] |
S. Bernard, J. Bélair and M. C. Mackey, Oscillations in cyclical neutropenia: New evidence based on mathematical modeling, Journal of Theoretical Biology, 223 (2003), 283-298, URL http://www.ams.org/mathscinet-getitem?mr=2079467.
doi: 10.1016/S0022-5193(03)00090-0. |
[9] |
S. Bernard, J. Bélair and M. C. Mackey, Bifurcations in a white-blood-cell production model, C. R. Biol., 327 (2004), 201-210, URL http://linkinghub.elsevier.com/retrieve/pii/S1631069104000381.
doi: 10.1016/j.crvi.2003.05.005. |
[10] |
F. J. Burns and I. F. Tannock, On the existence of a G$_0$-phase in the cell cycle, Cell Proliferation, 3 (1970), 321-334.
doi: 10.1111/j.1365-2184.1970.tb00340.x. |
[11] |
C. Colijn and M. C. Mackey, A mathematical model of hematopoiesis - I. Periodic chronic myelogenous leukemia, Journal of Theoretical Biology, 237 (2005), 117-132.
doi: 10.1016/j.jtbi.2005.03.033. |
[12] |
F. Ficara, M. J. Murphy, M. Lin and M. L. Cleary, Pbx1 regulates self-renewal of long-term hematopoietic stem cells by maintaining their quiescence, Cell Stem Cell, 2 (2008), 484-496, URL http://www.sciencedirect.com/science/article/pii/S1934590908001161.
doi: 10.1016/j.stem.2008.03.004. |
[13] |
K. Gu and Y. Liu, Lyapunov-Krasovskii functional for uniform stability of coupled differential-functional equations, Automatica, 45 (2009), 798-804.
doi: 10.1016/j.automatica.2008.10.024. |
[14] |
J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer New York, 1993.
doi: 10.1007/978-1-4612-4342-7. |
[15] |
Y. Kuang, Delay Differential Equations: With Applications in Population Dynamics, Academic Press, San Diego, 1993. |
[16] |
J. Lei and M. C. Mackey, Multistability in an age-structured model of hematopoiesis: Cyclical neutropenia, Journal of Theoretical Biology, 270 (2011), 143-153.
doi: 10.1016/j.jtbi.2010.11.024. |
[17] |
M. C. Mackey, Unified hypothesis for the origin of aplastic anemia and periodic hematopoiesis., Blood, 51 (1978), 941-956. |
[18] |
L. Pujo-Menjouet, S. Bernard and M. C. Mackey, Long period oscillations in a $G_0$ model of hematopoietic stem cells, SIAM J. Appl. Dyn. Syst., 4 (2005), 312-332.
doi: 10.1137/030600473. |
[19] |
L. Pujo-Menjouet and M. C. Mackey, Contribution to the study of periodic chronic myelogenous leukemia, C. R. Biol., 327 (2004), 235-244, URL http://linkinghub.elsevier.com/retrieve/pii/S1631069104000253.
doi: 10.1016/j.crvi.2003.05.004. |
[20] |
H. Takizawa, R. R. Regoes, C. S. Boddupalli, S. Bonhoeffer and M. G. Manz, Dynamic variation in cycling of hematopoietic stem cells in steady state and inflammation, J. Exp. Med., 208 (2011), 273-284, URL http://jem.rupress.org/content/208/2/273.full. |
[21] |
P. Vegh, J. Winckler and F. Melchers, Long-term "in vitro'' proliferating mouse hematopoietic progenitor cell lines, Immunology Letters, 130 (2010), 32-35, URL http://www.sciencedirect.com/science/article/pii/S0165247810000544.
doi: 10.1016/j.imlet.2010.02.001. |
[22] |
A. Wilson, E. Laurenti, G. Oser, R. C. van der Wath, W. Blanco-Bose, M. Jaworski, S. Offner, C. F. Dunant, L. Eshkind, E. Bockamp, P. Lió, H. R. MacDonald and A. Trumpp, Hematopoietic stem cells reversibly switch from dormancy to self-renewal during homeostasis and repair, Cell, 135 (2008), 1118-1129, URL http://www.sciencedirect.com/science/article/pii/S009286740801386X. |
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