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2003 | 13 | 3 | 289-296
Tytuł artykułu

Mathematical modeling of the competition between acquired immunity and cancer

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we propose and analyse a model of the competition between cancer and the acquired immune system. The model is a system of integro-differential bilinear equations. The role of the humoral response is analyzed. The simulations are related to the immunotherapy of tumors with antibodies.
Rocznik
Tom
13
Numer
3
Strony
289-296
Opis fizyczny
Daty
wydano
2003
otrzymano
2003-03-01
poprawiono
2003-06-01
Twórcy
  • Institute of Applied Mathematics and Mechanics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland
Bibliografia
  • Adam J.A. and Bellomo N. (Eds.) (1997): A Survey of Models for Tumor-Immune System Dynamics. - Boston: Birkhuser.
  • Arlotti L., Bellomo N. and Lachowicz M. (2000): Kinetic equations modelling population dynamics. - Transport Theory Statist. Phys., Vol. 29, No. 1-2, pp. 125-139.
  • Arlotti L., Gamba A. and Lachowicz M. (2002): A kinetic model of tumourim-mune system cellular interactions. - J. Theor.Medicine, Vol. 4, No. 1, pp. 39-50.
  • Bellomo N. and De Angelis E. (1998): Strategies of applied mathematics towards an immuno mathematical theory on tumors and immune system interactions. - Math. Models Meth. Appl. Sci., Vol. 8, No. 8, pp. 1403-1429.
  • Bellomo N. and Forni G. (1994): Dynamics of tumor interaction with the host immune system. - Math. Comput. Modell., Vol. 20, No. 1, pp. 107-122.
  • Bellomo N. and Preziosi L. (2000): Modelling and mathematical problems related to tumor evolution and its interaction with the immune system. - Math. Comput. Modell., Vol. 32, No. 3, pp. 413-452.
  • Bellomo N., Preziosi L. and Forni G. (1996): On a kinetic (cellular)theory of the competition between tumors and the immune host system. - J. Biol. Syst., Vol. 4, No. 4, pp. 479-502.
  • Bellomo B. and Pulvirenti M. (Eds.) (2000): Modeling in Applied Sciences. A Kinetic Theory Approach. - Boston: Birkhuser.
  • Chaplain M. (Ed.) (1999): Special issue on mathematical models for the growth, development and treatment of tumours. - Math. Models Meth. Appl. Sci., Vol. 9, No. 4.
  • Chen C.-H. and Wu T.-C. (1998): Experimental vaccine strategies for cancer immunotherapy. - J. Biomed. Sci., Vol. 5, No. 4, pp. 231-252.
  • De Angelis E. and Mesin L. (2001): Modelling of the immune response: conceptual frameworks and applications. - Math. Models Meth. Appl. Sci., Vol. 11, No. 9, pp. 1609-1630.
  • Kolev M. (2002a): A mathematical model of cellular immune response to leukemia. - Tech. Rep. RW 02-16 (116), November, 2002, Inst. Appl. Math. Mech., Warsaw University.
  • Kolev M. (2002b): On a mathematical model of humoral immune responseagainst cancer. - Proc. 8-th Nat. Conf. Application of Mathematics in Biology and Medicine, Łajs, Poland, pp. 75-81.
  • Kolev M. (2003): Mathematical modelling of the competition between tumors and immune system considering the role of the antibodies. - Math. Comput. Modell., (in print).
  • Kolev M., Kozłowska E. and Lachowicz M. (2002): A mathematical model for single cell cancer-immune system dynamics. - Tech. Rep. RW 02-05 (105), May, 2002, Inst. Appl.Math. Mech., Warsaw University.
  • Kuby J. (1997): Immunology, 3rd Ed.. - New York: W.H. Freeman.
  • Lachowicz M. (2000): Competition tumor-immune system. - Proc. 6-th Nat. Conf. Application of Mathematics in Biology and Medicine, Zawoja, Poland, pp. 89-93.
  • Lachowicz M. (2002): From microscopic to macroscopic description. Generalized kinetic equations. - Math. Models Meth. Appl. Sci., Vol. 12, No. 7, pp. 985-1005.
  • Lydyard P.M., Whelan A. and Fanger M.W. (2000): Instant Notes in Immunology. - Oxford: BIOS Scientific Publishers Ltd.
  • Moingeon P. (2001): Cancer vaccines. -Vaccine, Vol. 19, No. 11-12, pp. 1305-1326.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv13i3p289bwm
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