Stability analysis of models of cell production systems

Lajtha, 1962, Model of a bone-marrow stem-cell population, Bri. J. Haematol., 8, 442, 10.1111/j.1365-2141.1962.tb06548.x Wichmann, 1984 Potten, 1982, Evidence for discrete cell kinetic subpopulations in mouse epidermis based on mathematical analysis, Cell Tissue Kinet., 15, 305 Mackey, 1978, Unified hypothesis for the origin of aplastic anemia and periodic hematopoiesis, Blood, 51, 941, 10.1182/blood.V51.5.941.941 Wazewska-Czyzewska, 1976, Mathematical problems of the dynamics of the red-blood cell system (in Polish), Matematyka Stosowana, 6, 23 Aarnaes, 1979, A mathematical model of the control of red blood cell production, 309 Wichmann, 1983, Computer modeling of erythropoiesis, 100 Wichmann, 1982, A solution to the controversy on stem cell regulation, Blood Cells, 8, 461 M. Kimmel and O. Arino, Complex proliferative systems. Formal description and qualitative analysis. Syst. Sci. 9, no. 1–2, (to be published). Smith, 1973, Do cell cycle?, Proc. Natl. Acad. Sci. USA, 70, 1263, 10.1073/pnas.70.4.1263 Mitchison, 1971 Kimmel, 1979, Analysis of different variants of erythrocyte survival using digital computers, Acta Haematol. Polonica, 10, 1 Kimmel, 1982, Stochastic approach to the process of red cell destruction, Appl. Math., 17, 217 Kimmel, 1980, Cellular population dynamics I, Math. Biosci., 48, 211, 10.1016/0025-5564(80)90058-9 Kimmel, 1980, Cellular population dynamics II, Math. Biosci., 48, 225, 10.1016/0025-5564(80)90059-0 Kimmel, 1981, General theory of cell cycle dynamics based on branching processes in varying environment, 357 Loeffler, 1980, A comprehensive mathematical model of stem cell proliferation which reproduces most of the published experimental results, Cell Tissue Kinet., 13, 543 Hale, 1977 Hartman, 1964 Bellman, 1963 O. Arino and M. Kimmel, A model of competing feedbacks of the erythropoietic system with respect to system stability. Unpublished manuscript. Mackey, 1979, Periodic auto-immune hemolytic anemia: An induced dynamical disease, Bull. Math. Biol., 41, 829, 10.1007/BF02462379 Kaplan, 1977, On the non-linear differential delay equation x'(t) = −f(x(t), s(t − 1)), J. Diff. Eq., 23, 293, 10.1016/0022-0396(77)90132-2 Wheldon, 1975, Mathematical models of oscillatory blood cell production, Math. Biosci., 24, 289, 10.1016/0025-5564(75)90082-6 Nečas, 1976, Proliferation rate of haemopoietic stem cells after damage by several cytostatic agents, Cell Tissue Kinet., 9, 479 Nečas, 1977, Effect of hydroxyurea and vinblastine on the proliferation of the pluripotential stem cells, Neoplasma, 24, 29 Mackey, 1982, Continuous maturation of proliferating erythroid precursors, Cell Tissue Kinet., 15, 381 Wazeẘska-Czyzewska, 1976, Metoda badania kinetyki erytronu, Przeglad Metodyczny AM w Krakowie, X Chow, 1974, Existence of periodic solutions of autonomous functional differential equations, J. Diff. Eq., 15, 350, 10.1016/0022-0396(74)90084-9 Sikora, 1979, Numerical evaluation of roots of quasi-polynomials, Technical report of the Institute of Automation of the Warsaw Technical University Iscove, 1977, The role of erythropoietin in regulation of population size and cell cycling of early and late erythroid precursors in mouse bone marrow, Cell Tissue Kinet., 10, 323 Lord, 1981, The relationship of G0 to the cell cycle of haemopoietic spleen colony-forming cells, Cell Tissue Kinet., 14, 425 Clausen, 1984, Sub-populations of slowly cycling cells in S and G2 phase in mouse epidermis, Cell Tissue Kinet., 17, 351 Staiano-Coico, 1986, Human keratinocyte culture. Identification and staging of epidermal cell subpopulations, J. Clin Invest., 77, 396, 10.1172/JCI112317 M. Kimmel, Z. Darzynkiewicz, and L. Staiano-Coico, Stathmokinetic analysis of human epidermal cells in vitro. Cell Tissue Kinet. 19, (in press). Reincke, 1979, Forced differentiation of CFUs by iron 55 erythrocytocide, Blood Cells, 3, 351