Global asymptotic stability for an age-structured model of hematopoietic stem cell dynamics

References

• Cooke KL. Stability analysis for a vector disease model. Rocky Mountain J. Math. 1979;9:31–42.
   Google Scholar
• Aiello W, Freedman H, Wu J. Analysis of a model representing stage-structured population growth with state-dependent time delay. SIAM J. Appl. Math. 1992;52:855–869.
   Web of Science ®Google Scholar
• Mackey MC. Unified hypothesis for the origin of aplastic anemia and periodic hematopoiesis. Blood. 1978;51:941–956.
   PubMed Web of Science ®Google Scholar
• Adimy M, Crauste F, Ruan S. A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia. SIAM J. Appl. Math. 2005;65:1328–1352.
   Web of Science ®Google Scholar
• Kuang Y. Delay differential equations: with applications in population dynamics. Mathematics in science and engineering. Vol. 191, New York (NY): Academic Press; 1993.
   Google Scholar
• Smith HL. Reduction of structured population models to threshold-type delay equations and functional differential equations: a case study. Math. Biosci. 1993;113:1–23.
   PubMed Web of Science ®Google Scholar
• Pujo-Menjouet L, Mackey MC. Contribution to the study of periodic chronic myelogenous leukemia. C.R. Biol. 2004;327:235–244.
   PubMed Web of Science ®Google Scholar
• Pujo-Menjouet L, Bernard S, Mackey MC. Long period oscillations in a G0 model of hematopoietic stem cells. SIAM J. Appl. Dyn. Syst. 2005;4:312–332.
   Web of Science ®Google Scholar
• Adimy M, Crauste F. Global stability of a partial differential equation with distributed delay due to cellular replication. Nonlinear Anal.: Theory Methods Appl. 2003;54:1469–1491.
   Web of Science ®Google Scholar
• Adimy M, Crauste F. Modelling and asymptotic stability of a growth factor-dependent stem cell dynamics model with distributed delay. Discrete Contin. Dyn. Syst. Ser. B. 2007;8:19–38.
   Web of Science ®Google Scholar
• Adimy M, Crauste F, El Abdllaoui A. Discrete-maturity structured model of cell differentiation with applications to acute myelogenous leukemia. J. Biol. Syst. 2008;16:395–424.
   Web of Science ®Google Scholar
• Adimy M, Crauste F, Hbid M, et al. Stability and hopf bifurcation for a cell population model with state-dependent delay. SIAM J. Appl. Math. 2010;70:1611–1633.
   Web of Science ®Google Scholar
• Adimy M, Crauste F, Ruan S. Stability and hopf bifurcation in a mathematical model of pluripotent stem cell dynamics. Nonlinear Anal. Real World Appl. 2005;6:651–670.
   Web of Science ®Google Scholar
• Adimy M, Crauste F, Ruan S. Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases. Bull. Math. Biol. 2006;68:2321–2351.
   PubMed Web of Science ®Google Scholar
• Bradford GB, Williams B, Rossi R, et al. Quiescence, cycling, and turnover in the primitive hematopoietic stem cell compartment. Exp. Hematol. 1997;25:445–453.
   PubMed Web of Science ®Google Scholar
• Takizawa H, Regoes RR, Boddupalli CS, et al. Dynamic variation in cycling of hematopoietic stem cells in steady state and inflammation. J. Exp. Med. 2011;208:273–284.
   PubMed Web of Science ®Google Scholar
• Sachs L. The molecular control of hemopoiesis and leukemia. C.R. Acad. Sci. Paris Ser. III. 1993;316:871–891.
   PubMed Web of Science ®Google Scholar
• Iannelli M. Mathematical theory of age-structured population dynamics. Vol. 7, Applied mathematics monographs. Pisa: Giardini editori e stampatori; 1995.
   Google Scholar
• Gurtin ME, MacCamy RC. Non-linear age-dependent population dynamics. Arch. Ration. Mech. Anal. 1974;54:281–300.
   Web of Science ®Google Scholar
• Webb G. Theory of nonlinear age-dependent population dynamics. New York (NY): Marcel Dekker; 1985.
   Google Scholar
• Adimy M, Chekroun A, Touaoula T-M. A delay differential-difference system of hematopoietic stem cell dynamics. C.R. Math. 2015;353:303–307.
   Web of Science ®Google Scholar
• Hale JK, Cruz MA. Existence, uniqueness and continuous dependence for hereditary systems. Ann. Mat. Pura Appl. 1970;85:63–81.
   Google Scholar
• Hale JK, Verduyn Lunel SM. Introduction to functional differential equations. Vol. 99, Applied mathematical sciences. New York (NY): Springer-Verlag; 1993.
   Google Scholar
• Gu K, Liu Y. Lyapunov--Krasovskii functional for uniform stability of coupled differential-functional equations. Automatica. 2009;45:798–804.
   Web of Science ®Google Scholar
• Pepe P, Jiang Z-P, Fridman E. A new Lyapunov--Krasovskii methodology for coupled delay differential and difference equations. Int. J. Control. 2008;81:107–115.
   Web of Science ®Google Scholar
• Cruz MA, Hale JK. Stability of functional differential equations of neutral type. J. Differ. Equ. 1970;7:334–355.
   Web of Science ®Google Scholar