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Volumn 67, Issue 2, 2006, Pages 387-407

Stochastic differential delay equation, moment stability, and application to hematopoietic stem cell regulation system

Author keywords

Hematopoietic disease; Moment stability; Stochastic differential delay equation

Indexed keywords

CELLS; CONVERGENCE OF NUMERICAL METHODS; LAPLACE TRANSFORMS; METHOD OF MOMENTS; RANDOM PROCESSES; WHITE NOISE;

EID: 34247603905     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/060650234     Document Type: Article
Times cited : (79)

References (59)
  • 1
    • 0028358438 scopus 로고
    • The relationship of erythropoietin and iron metabolism to red blood cell production in humans
    • J. W. ADAMSON, The relationship of erythropoietin and iron metabolism to red blood cell production in humans, Sem. Oncol., 21 (1994), pp. 9-15.
    • (1994) Sem. Oncol , vol.21 , pp. 9-15
    • ADAMSON, J.W.1
  • 2
    • 24944579472 scopus 로고    scopus 로고
    • Stochastic stabilisation of functional differential equations
    • J. APPLEBY AND X. MAO, Stochastic stabilisation of functional differential equations, Systems Control Lett., 54 (2005), pp. 1069 - 1081.
    • (2005) Systems Control Lett , vol.54 , pp. 1069-1081
    • APPLEBY, J.1    MAO, X.2
  • 4
    • 1242287590 scopus 로고    scopus 로고
    • Asymptotic properties of a delay differential equation model for the interaction of glucose with plasma and interstitial insulin
    • D. L. BENNETT AND S. A. GOURLEY, Asymptotic properties of a delay differential equation model for the interaction of glucose with plasma and interstitial insulin, Appl. Math. Comput., 151 (2004), pp. 189-207.
    • (2004) Appl. Math. Comput , vol.151 , pp. 189-207
    • BENNETT, D.L.1    GOURLEY, S.A.2
  • 5
    • 0037678721 scopus 로고    scopus 로고
    • Oscillations in cyclical neutropenia: New evidence based on mathematical modeling
    • S. BERNARD, J. BÉLAIR, AND M. C. MACKEY, Oscillations in cyclical neutropenia: New evidence based on mathematical modeling, J. Theoret. Biol., 223 (2003), pp. 283-298.
    • (2003) J. Theoret. Biol , vol.223 , pp. 283-298
    • BERNARD, S.1    BÉLAIR, J.2    MACKEY, M.C.3
  • 7
    • 26044443571 scopus 로고    scopus 로고
    • A mathematical model of hematopoiesis: I. Periodic chronic myelogenous leukemia
    • C. COLIJIN AND M. C. MACKEY, A mathematical model of hematopoiesis: I. Periodic chronic myelogenous leukemia, J. Theoret. Biol., 237 (2005), pp. 117-132.
    • (2005) J. Theoret. Biol , vol.237 , pp. 117-132
    • COLIJIN, C.1    MACKEY, M.C.2
  • 8
    • 26044442893 scopus 로고    scopus 로고
    • A mathematical model of hematopoiesis: II. Cyclical neutropenia
    • C. COLIJIN AND M. C. MACKEY, A mathematical model of hematopoiesis: II. Cyclical neutropenia, J. Theoret. Biol., 237 (2005), pp. 133-146.
    • (2005) J. Theoret. Biol , vol.237 , pp. 133-146
    • COLIJIN, C.1    MACKEY, M.C.2
  • 9
    • 39649091518 scopus 로고    scopus 로고
    • Bifurcation and bistability in a model of hematopoietic regulation
    • submitted
    • C. COLIJIN AND M. C. MACKEY, Bifurcation and bistability in a model of hematopoietic regulation, SIAM J. Appl. Dyn. Syst., submitted.
    • SIAM J. Appl. Dyn. Syst
    • COLIJIN, C.1    MACKEY, M.C.2
  • 12
    • 0032956844 scopus 로고    scopus 로고
    • Periodic chronic myelogenous leukaemia: Spectral analysis of blood cell counts and aetiological implications
    • P. FORTIN AND M. C. MACKEY, Periodic chronic myelogenous leukaemia: Spectral analysis of blood cell counts and aetiological implications, Br. J. Haematol., 104 (1999), pp. 336-345.
    • (1999) Br. J. Haematol , vol.104 , pp. 336-345
    • FORTIN, P.1    MACKEY, M.C.2
  • 13
    • 0036706324 scopus 로고    scopus 로고
    • Relaxation oscillations in a class of delay differential equations
    • A. C. FOWLER AND M. C. MACKEY, Relaxation oscillations in a class of delay differential equations, SIAM J. Appl. Math., 63 (2002), pp. 299-323.
    • (2002) SIAM J. Appl. Math , vol.63 , pp. 299-323
    • FOWLER, A.C.1    MACKEY, M.C.2
  • 15
    • 0018373214 scopus 로고
    • Pathological conditions resulting from instabilities in physiological control systems
    • L. GLASS AND M. C. MACKEY, Pathological conditions resulting from instabilities in physiological control systems, Ann. New York Acad. Sci., 316 (1979), pp. 214-235.
    • (1979) Ann. New York Acad. Sci , vol.316 , pp. 214-235
    • GLASS, L.1    MACKEY, M.C.2
  • 17
    • 19944390652 scopus 로고    scopus 로고
    • A delay reaction-diffusion model of the spread of bacteriophage infection
    • S. A. GOURLEY AND Y. KUANG, A delay reaction-diffusion model of the spread of bacteriophage infection, SIAM J. Appl. Math., 65 (2005), pp. 550-566.
    • (2005) SIAM J. Appl. Math , vol.65 , pp. 550-566
    • GOURLEY, S.A.1    KUANG, Y.2
  • 21
    • 0032532631 scopus 로고    scopus 로고
    • Cyclical neutropenia and other periodic hematological diseases: A review of mechanisms and mathematical models
    • C. HAURIE, D. C. DALE, AND M. C. MACKEY, Cyclical neutropenia and other periodic hematological diseases: A review of mechanisms and mathematical models, Blood, 92 (1998), pp. 2629-2640.
    • (1998) Blood , vol.92 , pp. 2629-2640
    • HAURIE, C.1    DALE, D.C.2    MACKEY, M.C.3
  • 22
    • 0033052104 scopus 로고    scopus 로고
    • Occurrence of periodic oscillations in the differential blood counts of congenital, idiopathic and cyclical neutropenic patients before and during treatment with G-CSF
    • C. HAURIE, M. C. MACKEY, AND D. C. DALE, Occurrence of periodic oscillations in the differential blood counts of congenital, idiopathic and cyclical neutropenic patients before and during treatment with G-CSF, Exper. Hematol., 27 (1997), pp. 401-409.
    • (1997) Exper. Hematol , vol.27 , pp. 401-409
    • HAURIE, C.1    MACKEY, M.C.2    DALE, D.C.3
  • 24
    • 0002447873 scopus 로고
    • On stationary solutions of a stochastic differential equations
    • K. ITO AND M. NISIO, On stationary solutions of a stochastic differential equations, J. Math. Kyoto Univ., 4 (1964), pp. 1-75.
    • (1964) J. Math. Kyoto Univ , vol.4 , pp. 1-75
    • ITO, K.1    NISIO, M.2
  • 25
    • 34247642456 scopus 로고    scopus 로고
    • Theory, stochastic stability and applications of stochastic delay differential equations: A survey of results
    • A. F. IVANOV, Y. I. KAZMERCHUK, AND A. V. SWISHCHUK, Theory, stochastic stability and applications of stochastic delay differential equations: A survey of results, Differential Equations Dynam. Systems, 11 (2003), pp. 55-115.
    • (2003) Differential Equations Dynam. Systems , vol.11 , pp. 55-115
    • IVANOV, A.F.1    KAZMERCHUK, Y.I.2    SWISHCHUK, A.V.3
  • 27
    • 0001840597 scopus 로고
    • Langevin's stochastic differential equation extended by a time-delayed term
    • U. KÜCHLER AND B. MENSCH, Langevin's stochastic differential equation extended by a time-delayed term, Stochastics Stochastics Rep., 40 (1992), pp. 23-42.
    • (1992) Stochastics Stochastics Rep , vol.40 , pp. 23-42
    • KÜCHLER, U.1    MENSCH, B.2
  • 29
    • 32144432198 scopus 로고    scopus 로고
    • Effects of noise on nonlinear dynamics
    • A. Beuter, L. Glass, M. C. Mackey, and M. S. Titcombe, eds, Springer-Verlag, New York
    • A. LONGTIN, Effects of noise on nonlinear dynamics, in Nonlinear Dynamics in Physiology and Medicine, A. Beuter, L. Glass, M. C. Mackey, and M. S. Titcombe, eds., Springer-Verlag, New York, 2003, pp. 149-189.
    • (2003) Nonlinear Dynamics in Physiology and Medicine , pp. 149-189
    • LONGTIN, A.1
  • 31
    • 0018138249 scopus 로고
    • Unified hypothesis for the origin of aplastic anemia and periodic haematopoiesis
    • M. C. MACKEY, Unified hypothesis for the origin of aplastic anemia and periodic haematopoiesis, Blood, 51 (1978), pp. 941-956.
    • (1978) Blood , vol.51 , pp. 941-956
    • MACKEY, M.C.1
  • 32
    • 0003117329 scopus 로고
    • Dynamic haematological disorders of stem cell origin
    • J. G. Vassileva-Popova and E. V. Jensen, eds, Plenum Publishing, New York
    • M. C. MACKEY, Dynamic haematological disorders of stem cell origin, in Biophysical and Biochemical Information Transfer in Recognition, J. G. Vassileva-Popova and E. V. Jensen, eds., Plenum Publishing, New York, 1979, pp. 373-409.
    • (1979) Biophysical and Biochemical Information Transfer in Recognition , pp. 373-409
    • MACKEY, M.C.1
  • 33
    • 0018570535 scopus 로고
    • Periodic auto-immune hemolytic anemia: An induced dynamical disease
    • M. C. MACKEY, Periodic auto-immune hemolytic anemia: An induced dynamical disease, Bull. Math. Biol., 41 (1979), pp. 829-834.
    • (1979) Bull. Math. Biol , vol.41 , pp. 829-834
    • MACKEY, M.C.1
  • 34
    • 0002289939 scopus 로고
    • Dynamic diseases and bifurcations in physiological control systems
    • M. C. MACKEY AND U. VAN DER HEIDEN, Dynamic diseases and bifurcations in physiological control systems, Funk. Biol. Med., 1 (1982), pp. 156-164.
    • (1982) Funk. Biol. Med , vol.1 , pp. 156-164
    • MACKEY, M.C.1    VAN DER HEIDEN, U.2
  • 35
    • 84982593772 scopus 로고
    • Continuous maturation of proliferating erythroid precursors
    • M. C. MACKEY AND P. DÖRMER, Continuous maturation of proliferating erythroid precursors, Cell Tissue Kinet., 15 (1982), pp. 381-392.
    • (1982) Cell Tissue Kinet , vol.15 , pp. 381-392
    • MACKEY, M.C.1    DÖRMER, P.2
  • 37
    • 0000478221 scopus 로고
    • Feedback, delays, and the origins of blood cell dynamics
    • M. C. MACKEY AND J. G. MILTON, Feedback, delays, and the origins of blood cell dynamics, Comm. Theoret. Biol., 1 (1990), pp. 299-237.
    • (1990) Comm. Theoret. Biol , vol.1 , pp. 299-237
    • MACKEY, M.C.1    MILTON, J.G.2
  • 38
    • 5544262166 scopus 로고
    • Solution moment stability in stochastic differential delay equations
    • M. C. MACKEY AND I. G. NECHAEVA, Solution moment stability in stochastic differential delay equations, Phys. Rev. E (3), 52 (1995), pp. 3366-3376.
    • (1995) Phys. Rev. E , vol.52 , Issue.3 , pp. 3366-3376
    • MACKEY, M.C.1    NECHAEVA, I.G.2
  • 39
    • 0035030264 scopus 로고    scopus 로고
    • Cell kinetic status of haematopoietic stem cells
    • M. C. MACKEY, Cell kinetic status of haematopoietic stem cells, Cell Prolif., 43 (2001), pp. 71-83.
    • (2001) Cell Prolif , vol.43 , pp. 71-83
    • MACKEY, M.C.1
  • 42
    • 0035582005 scopus 로고    scopus 로고
    • Almost sure exponential stability of delay equations with damped stochastic perturbation
    • X. MAO, Almost sure exponential stability of delay equations with damped stochastic perturbation, Stoch. Anal. Appl., 19 (2001), pp. 67-84.
    • (2001) Stoch. Anal. Appl , vol.19 , pp. 67-84
    • MAO, X.1
  • 43
    • 0037293686 scopus 로고    scopus 로고
    • Numerical solutions of stochastic differential delay equations under local Lipschitz condition
    • X. MAO AND S. SABANIS, Numerical solutions of stochastic differential delay equations under local Lipschitz condition, J. Comput. Appl. Math., 151 (2003), pp. 215-227.
    • (2003) J. Comput. Appl. Math , vol.151 , pp. 215-227
    • MAO, X.1    SABANIS, S.2
  • 44
    • 24344494472 scopus 로고    scopus 로고
    • Khasminskii-type theorems for stochastic differential delay equations
    • X. MAO AND M. J. RASSIAS, Khasminskii-type theorems for stochastic differential delay equations, Stoch. Anal. Appl., 23 (2005), pp. 1045-1069.
    • (2005) Stoch. Anal. Appl , vol.23 , pp. 1045-1069
    • MAO, X.1    RASSIAS, M.J.2
  • 45
    • 0024956064 scopus 로고
    • Periodic haematological diseases: Mystical entities or dynamical disorders?
    • J. G. MILTON AND M. C. MACKEY, Periodic haematological diseases: Mystical entities or dynamical disorders?, J. Roy. Coll. Phys. (Lond.), 23 (1989), pp. 236-241.
    • (1989) J. Roy. Coll. Phys. (Lond.) , vol.23 , pp. 236-241
    • MILTON, J.G.1    MACKEY, M.C.2
  • 46
    • 0025633911 scopus 로고
    • Complex dynamics and noise in simple neural networks with delayed mixed feedback
    • J. G. MILTON, U. VAN DER HEIDEN, A. LONGTIN, AND M. C. MACKEY, Complex dynamics and noise in simple neural networks with delayed mixed feedback, Biomed. Biochim. Acta, 49 (1990), pp. 697-707.
    • (1990) Biomed. Biochim. Acta , vol.49 , pp. 697-707
    • MILTON, J.G.1    VAN DER HEIDEN, U.2    LONGTIN, A.3    MACKEY, M.C.4
  • 48
    • 34247597556 scopus 로고    scopus 로고
    • B. ØKSENDAL, Stochastic Differential Equations: An Introduction with Applications, 6th ed., Springer-Verlag, New York, 2003.
    • B. ØKSENDAL, Stochastic Differential Equations: An Introduction with Applications, 6th ed., Springer-Verlag, New York, 2003.
  • 49
    • 0029682095 scopus 로고    scopus 로고
    • S. PAVORD, M. SIVAKUMARAN, P. FURBER, AND V. MITCHELL, Cyclical thrombocytopenia as a rare manifestation of myelodysplastic syndrome, Clin. Lab. Haematol., 18 (1996), pp. 221-223.
    • S. PAVORD, M. SIVAKUMARAN, P. FURBER, AND V. MITCHELL, Cyclical thrombocytopenia as a rare manifestation of myelodysplastic syndrome, Clin. Lab. Haematol., 18 (1996), pp. 221-223.
  • 50
    • 0030003411 scopus 로고    scopus 로고
    • Effect of recombinant granulocyte colonystimulating factor on neutrophil kinetics in normal young and elderly humans
    • T .H. PRICE, G. S. CHATTA, AND D. C. DALE, Effect of recombinant granulocyte colonystimulating factor on neutrophil kinetics in normal young and elderly humans, Blood, 88 (1996), pp. 335-340.
    • (1996) Blood , vol.88 , pp. 335-340
    • PRICE, T.H.1    CHATTA, G.S.2    DALE, D.C.3
  • 52
    • 1842426546 scopus 로고    scopus 로고
    • Contribution to the study of periodic chronic myelogenous leukemia
    • L. PUJO-MENJOUET AND M. C. MACKEY, Contribution to the study of periodic chronic myelogenous leukemia, C.R. Biol., 327 (2004), pp. 235-244.
    • (2004) C.R. Biol , vol.327 , pp. 235-244
    • PUJO-MENJOUET, L.1    MACKEY, M.C.2
  • 54
    • 0034699773 scopus 로고    scopus 로고
    • Regulation of platelet production: The normal response to perturbation and cyclical platelet disease
    • M. SANTILLAN, J. M. MAHAFFY, J. BELAIR. AND M. C. MACKEY, Regulation of platelet production: The normal response to perturbation and cyclical platelet disease, J. Theoret. Biol., 206 (2000), pp. 585-603.
    • (2000) J. Theoret. Biol , vol.206 , pp. 585-603
    • SANTILLAN, M.1    MAHAFFY, J.M.2    BELAIR, J.3    MACKEY, M.C.4
  • 55
    • 0029794641 scopus 로고    scopus 로고
    • Erythropoietin can promote erythroid progenitor survival by repressing apoptosis through bcl-1 and bcl-2
    • M. SILVA, D. GRILLOT, A. BENITO, C. RICHARD, G. NUNEZ, AND J. FERNANDEZ-LUNA, Erythropoietin can promote erythroid progenitor survival by repressing apoptosis through bcl-1 and bcl-2, Blood, 88 (1996), pp. 1576-1582.
    • (1996) Blood , vol.88 , pp. 1576-1582
    • SILVA, M.1    GRILLOT, D.2    BENITO, A.3    RICHARD, C.4    NUNEZ, G.5    FERNANDEZ-LUNA, J.6
  • 57
    • 0001736303 scopus 로고
    • A new representation for stochastic integrals and equations
    • R. L. STRATONOVICH, A new representation for stochastic integrals and equations, SIAM J. Control, 4 (1966), pp. 362-371.
    • (1966) SIAM J. Control , vol.4 , pp. 362-371
    • STRATONOVICH, R.L.1
  • 58
    • 0030884466 scopus 로고    scopus 로고
    • Recombinant human c-Mpl ligand (thrombopoietin) not only acts on megakaryocyte progenitors, but also on erythroid and multipotential progenitors in vitro
    • S. TANIMUKAI, T. KIMURA, H. SAKABE, Y. OHMIZONO, T. KATO, H. MIYAZAKI, H. YAMAGISHI, AND Y. SONODA, Recombinant human c-Mpl ligand (thrombopoietin) not only acts on megakaryocyte progenitors, but also on erythroid and multipotential progenitors in vitro, Exp. Hematol., 25 (1997), pp. 1025-1033.
    • (1997) Exp. Hematol , vol.25 , pp. 1025-1033
    • TANIMUKAI, S.1    KIMURA, T.2    SAKABE, H.3    OHMIZONO, Y.4    KATO, T.5    MIYAZAKI, H.6    YAMAGISHI, H.7    SONODA, Y.8
  • 59
    • 0017571148 scopus 로고
    • Cyclical thrombocytopenia with remission during lynestrenol treatment in a woman
    • P. WAHLBERG, D. NYMAN, P. EKELUND, S. A. CARLSSON, AND H. GRANLUND, Cyclical thrombocytopenia with remission during lynestrenol treatment in a woman, Ann. Clin. Res., 9 (1977), pp. 356-358.
    • (1977) Ann. Clin. Res , vol.9 , pp. 356-358
    • WAHLBERG, P.1    NYMAN, D.2    EKELUND, P.3    CARLSSON, S.A.4    GRANLUND, H.5


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