American Institute of Mathematical Sciences

Advanced
2011, 2011(Special): 32-43. doi: 10.3934/proc.2011.2011.32

A model for stem cell population dynamics with regulated maturation delay

Tomas Alarcon 1, , Philipp Getto 2, , Anna Marciniak-Czochra 3, and  Maria dM Vivanco 4,

1. 

Centre de Recerca Matem, Campus de Bellaterra, Edifici C, 08193 Bellaterra, Barcelona, Spain
2. 

BCAM (Basque Center For Applied Mathematics), Bizkaia Technology Park, Building 500, E-48160 Derio, Spain
3. 

University of Heidelberg, Interdisciplinary Center for Scientific Computing (IWR), Institute of Applied Mathematics and BIOQUANT, Im Neuenheimer Feld 267, 69120 Heidelberg
4. 

CIC BioGUNE, Bizkaia Technology Park, Building 801 A, E-48160 Derio, Spain

Received  July 2010 Revised  April 2011 Published  September 2011

We develop a structured population model for the maturation process of stem cells in the form of a state-dependent delay di erential equation. Moreover, results on existence, uniqueness and positivity of solutions as well as conditions of existence for equilibria and representations of these are established. We give biological interpretations for the conditions of existence of equilibria.
Keywords: state-dependent delay di erential equation, stem cells, structured population model.
Mathematics Subject Classification: Primary: 34K05; Secondary: 92B05.
Citation: Tomas Alarcon, Philipp Getto, Anna Marciniak-Czochra, Maria dM Vivanco. A model for stem cell population dynamics with regulated maturation delay. Conference Publications, 2011, 2011 (Special) : 32-43. doi: 10.3934/proc.2011.2011.32
[1]

Shangzhi Li, Shangjiang Guo. Dynamics of a stage-structured population model with a state-dependent delay. Discrete and Continuous Dynamical Systems - B, 2020, 25 (9) : 3523-3551. doi: 10.3934/dcdsb.2020071
[2]

A. R. Humphries, O. A. DeMasi, F. M. G. Magpantay, F. Upham. Dynamics of a delay differential equation with multiple state-dependent delays. Discrete and Continuous Dynamical Systems, 2012, 32 (8) : 2701-2727. doi: 10.3934/dcds.2012.32.2701
[3]

Matthias Büger, Marcus R.W. Martin. Stabilizing control for an unbounded state-dependent delay equation. Conference Publications, 2001, 2001 (Special) : 56-65. doi: 10.3934/proc.2001.2001.56
[4]

Qingwen Hu. A model of regulatory dynamics with threshold-type state-dependent delay. Mathematical Biosciences & Engineering, 2018, 15 (4) : 863-882. doi: 10.3934/mbe.2018039
[5]

Yunfei Lv, Rong Yuan, Yuan He. Wavefronts of a stage structured model with state--dependent delay. Discrete and Continuous Dynamical Systems, 2015, 35 (10) : 4931-4954. doi: 10.3934/dcds.2015.35.4931
[6]

Hans-Otto Walther. On Poisson's state-dependent delay. Discrete and Continuous Dynamical Systems, 2013, 33 (1) : 365-379. doi: 10.3934/dcds.2013.33.365
[7]

István Györi, Ferenc Hartung. Exponential stability of a state-dependent delay system. Discrete and Continuous Dynamical Systems, 2007, 18 (4) : 773-791. doi: 10.3934/dcds.2007.18.773
[8]

Shangzhi Li, Shangjiang Guo. Dynamics of a two-species stage-structured model incorporating state-dependent maturation delays. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1393-1423. doi: 10.3934/dcdsb.2017067
[9]

Josef Diblík. Long-time behavior of positive solutions of a differential equation with state-dependent delay. Discrete and Continuous Dynamical Systems - S, 2020, 13 (1) : 31-46. doi: 10.3934/dcdss.2020002
[10]

Benjamin B. Kennedy. A state-dependent delay equation with negative feedback and "mildly unstable" rapidly oscillating periodic solutions. Discrete and Continuous Dynamical Systems - B, 2013, 18 (6) : 1633-1650. doi: 10.3934/dcdsb.2013.18.1633
[11]

Guo Lin, Haiyan Wang. Traveling wave solutions of a reaction-diffusion equation with state-dependent delay. Communications on Pure and Applied Analysis, 2016, 15 (2) : 319-334. doi: 10.3934/cpaa.2016.15.319
[12]

Benjamin B. Kennedy. A periodic solution with non-simple oscillation for an equation with state-dependent delay and strictly monotonic negative feedback. Discrete and Continuous Dynamical Systems - S, 2020, 13 (1) : 47-66. doi: 10.3934/dcdss.2020003
[13]

Alexander Rezounenko. Stability of a viral infection model with state-dependent delay, CTL and antibody immune responses. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1547-1563. doi: 10.3934/dcdsb.2017074
[14]

Alexander Rezounenko. Viral infection model with diffusion and state-dependent delay: Stability of classical solutions. Discrete and Continuous Dynamical Systems - B, 2018, 23 (3) : 1091-1105. doi: 10.3934/dcdsb.2018143
[15]

Ovide Arino, Eva Sánchez. A saddle point theorem for functional state-dependent delay differential equations. Discrete and Continuous Dynamical Systems, 2005, 12 (4) : 687-722. doi: 10.3934/dcds.2005.12.687
[16]

Tibor Krisztin. A local unstable manifold for differential equations with state-dependent delay. Discrete and Continuous Dynamical Systems, 2003, 9 (4) : 993-1028. doi: 10.3934/dcds.2003.9.993
[17]

Benjamin B. Kennedy. Multiple periodic solutions of state-dependent threshold delay equations. Discrete and Continuous Dynamical Systems, 2012, 32 (5) : 1801-1833. doi: 10.3934/dcds.2012.32.1801
[18]

Qingwen Hu, Bernhard Lani-Wayda, Eugen Stumpf. Preface: Delay differential equations with state-dependent delays and their applications. Discrete and Continuous Dynamical Systems - S, 2020, 13 (1) : i-i. doi: 10.3934/dcdss.20201i
[19]

Eugen Stumpf. Local stability analysis of differential equations with state-dependent delay. Discrete and Continuous Dynamical Systems, 2016, 36 (6) : 3445-3461. doi: 10.3934/dcds.2016.36.3445
[20]

Ismael Maroto, Carmen NÚÑez, Rafael Obaya. Dynamical properties of nonautonomous functional differential equations with state-dependent delay. Discrete and Continuous Dynamical Systems, 2017, 37 (7) : 3939-3961. doi: 10.3934/dcds.2017167

 Impact Factor: 

Tools

Metrics

  • PDF downloads (137)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy