Article PDF
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
Literature Cited
R. T. Prenh, “Review/commentary: The dose-response curve in tumor-immunity,” Int. J. Immunopharmacology,5, No. 4, 255–257 (1983).
M. E. Colmeraver, I. A. Koziol, and V. H. Pilch, “Enhancement of metastasis development by BCG immunotherapy,” J. Surg. Oncology,15, No. 3, 235–241 (1980).
E. F. Wheelock, K. Weinhold, and I. Levich, “The tumor formant state,” Adv. Cancer Res.,34, 107–135 (1981).
A. Alsabti, “Tumor dormancy: A review,” Tumor Res.,13, 1–13 (1978).
N. V. Stepanov and Yu. M. Romanovskii, “Classification of mathematical models in microbiology and methods of their analysis,” in: Applications of Mathematical Methods in Microbiology [in Russian], Otd. NTI, VTs AN SSSR, Pushchino (1975), pp. 3–26.
G. de Lisi and R. Rescigno, “Immune surveillance and neoplasia, 1: A minimal mathematical model,” Bull. Math. Biol.,39, Nos. 1/2, 201–202 (1977).
R. Rescigno and G. de Lisi, “Immune surveillance and neoplasia, 2: A two-stage mathematical model,” Bull. Math. Biol.,39, Nos. 3/4, 487–497 (1977).
R. P. Garay and R. Lefever, “A kinetic approach to the immunology of cancer: Stationary states properties of effector-target cell reactions,” J. Theor. Biol.,73, No. 2, 417–438 (1978).
V. A. Kuznetsov and M. V. Vol'kenshtein, “A mathematical model of cell immune response to tumor growth,” in: Proceedings of the Third National Conference on Biology and Medical Cybernetics (Sukhumi, October 1978) [in Russian], Vol. 1, Akad. Nauk SSSR, Moscow (1978), pp. 58–61.
V. A. Kuznetsov, “Dynamics of immune cell antitumor responses, 1: Synthesis of a multilevel model,” in: Mathematical Methods of Systems Theory [in Russian], Kirg. Gos. Un-t, Frunze (1979), Issue 1, pp. 57–71.
V. A. Kuznetsov and M. V. Vol'kenshtein, “Dynamics of immune cell antitumor responses, 2: Qualitative analysis of the model,” in: Mathematical Methods of Systems Theory [in Russian], Kirg. Gos. Un-t, Frunze (1979), Issue 1, pp. 72–100.
V. A. Kuznetsov, “Bifurcations in a model of two-level reactivity of the immune system to the antigens of a developing neoplasm,” in: Dynamics of Biological Populations [in Russian], Gorky Gos. Un-t, Gor'kii (1983), pp. 52–64.
V. A. Kuznetsov, “Analysis of cell populations manifesting natural resistance to tumors,” Immunologiya, No. 3, 43–51 (1984).
V. V. Ivanov, V. M. Yanenko, K. L. Atoev, et al., “Mathematical modeling of the interaction of lymphocytes with tumor cells,” in: System Simulation in Biology and Medicine [in Russian], Dom Tekhniki, Prague (1986).
R. V. Petrov, I. M. Dozmorov, G. V. Lutsenko, et al., “Two-phase interaction of T-lymphocytes with allogenic stem cells,” Immunologiya, No. 4, 16–19 (1985).
Z. Grossman and G. Berke, “Tumor escape from immunoelimination,” J. Theor. Biol.,83, No. 2, 267–269 (1980).
G. I. Deichman, “Modern concepts of immunological relationships of a tumor and the body,” in: Tumor Growth as a Problem of Developmental Biology [in Russian], Nauka, Moscow (1979), pp. 208–230.
R. J. de Boer and P. Hogeweg, “Tumor escape immune elimination: Simplified precursor bound cytotoxicity models,” J. Theor. Biol.,113, No. 4, 719–736 (1985).
R. J. de Boer and P. Hogeweg, “Implications of macrophage/T-lymphocyte interactions for tumor rejectability,” in: Immunology and Epidemiology, G. W. Hoffman and T. Hraba (eds.), Springer, Berlin-New York (1985), pp. 120–140.
A. M. Molchanov, “Multibarrier immunity,” Biofizika,16, No. 4, 482–486 (1971).
V. A. Kuznetsov and M. V. Vol'kenshtein, “Analysis of the potential forms of behavior of the kinetics of cytotoxic cell antitumor responses,” in: Immunity and Allergy in Infectional and Noninfectional Pathology [in Russian], Ilim, Frunze (1980), pp. 62–64.
N. M. Émanuel, “Chemical and biological kinetics,” Uspekhi Khimii,50, No. 10, 1721–1809 (1981).
A. S. Belokhvostov and B. O. Voitenkov, “The role of immunosuppressive factors of tumors in three stages of immune interactions in an organism,” Uspekhi Sovrem. Biologii,95, No. 2, 255–272 (1983).
R. J. North, “The murine antitumor immune response and its therapeutic manipulation,” Adv. Immunol.,35, 89–154 (1984).
G. I. Marchuk, Mathematical Models in Immunology [in Russian], Nauka, Moscow (1980).
Kh. Guretskii, Analysis and Synthesis of Control Systems with Delays [in Russian], Mashinostroenie, Moscow (1974).
B. F. Dibrov, M. A. Lifschits, and M. V. Volkenstein, “Mathematical model of immune process,” J. Theor. Biol.,65, No. 4, 609–631 (1977).
V. M. Yanenko and V. A. Mazurenko, “Simulation of the mechanisms regulating the interaction of hemopoietic elements in the course of leukosis,” in: Mathematical Models in Immunology and Medicine [Russian translation], Mir, Moscow (1986), pp. 223–229.
A. Bastin, R. H. Loblei, R. D. Trent, et al., “Suppressor T-cells in homeostasis of the immune system and in pathology,” in: Recent Developments in Clinical Immunology [in Russian], Meditsina, Moscow (1983), pp. 54–95.
Additional information
Translated from Kibernetika, No. 4, pp. 96–102, July–August, 1987.
Rights and permissions
About this article
Cite this article
Kuznetsov, V.A. Mathematical modeling of the development of dormant tumors and immune stimulation of their growth. Cybern Syst Anal 23, 556–564 (1987). https://doi.org/10.1007/BF01078916
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01078916