Mathematical Modeling of the Competition Between Acquired Immunity and Cancer

• Autorzy: Kolev M.
• 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.

Słowa kluczowe

EN

leukemia; acquired immunity; immunotherapy; antibodies; integro-differential equations

PL

białaczka; odporność nabyta; immunoterapia; równanie różniczkowe

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2003
• Tom: Vol. 13, no 3
• Strony: 289--296
• Opis fizyczny: Bibliogr. 20 poz., wykr.

Twórcy

autor

Kolev M.

• Institute of Applied Mathematics and Mechanics Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland; South-West University, Blagoevgrad, Bulgaria,

Bibliografia

• [1] Adam J.A. and Bellomo N. (Eds.) (1997): A Survey of Models for Tumor–Immune System Dynamics. — Boston: Birkhäuser.
• [2] 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.
• [3] Arlotti L., Gamba A. and Lachowicz M. (2002): A kinetic model of tumour/immune system cellular interactions. — J. Theor. Medicine, Vol. 4, No. 1, pp. 39–50.
• [4] 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.
• [5] 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.
• [6] 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.
• [7] 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.
• [8] Bellomo B. and Pulvirenti M. (Eds.) (2000): Modeling in Applied Sciences. A Kinetic Theory Approach. — Boston: Birkhäuser.
• [9] 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.
• [10] Chen C.-H. and Wu T.-C. (1998): Experimental vaccine strategies for cancer immunotherapy.—J. Biomed. Sci., Vol. 5, No. 4, pp. 231–252.
• [11] 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.
• [12] 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.
• [13] Kolev M. (2002b): On a mathematical model of humoral immune response against cancer. — Proc. 8-th Nat. Conf. Application of Mathematics in Biology and Medicine, Łajs, Poland, pp. 75–81.
• [14] Kolev M. (2003): Mathematical modelling of the competition between tumors and immune system considering the role of the antibodies.—Math. Comput. Modell., (in print).
• [15] 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.
• [16] Kuby J. (1997): Immunology, 3rd Ed..—New York: W.H. Freeman.
• [17] Lachowicz M. (2000): Competition tumor–immune system. — Proc. 6-th Nat. Conf. Application of Mathematics in Biology and Medicine, Zawoja, Poland, pp. 89–93.
• [18] Lachowicz M. (2002): From microscopic to macroscopic description. Generalized kinetic equations. — Math. Models Meth. Appl. Sci., Vol. 12, No. 7, pp. 985–1005.
• [19] Lydyard P.M., Whelan A. and Fanger M.W. (2000): Instant Notes in Immunology. — Oxford: BIOS Scientific Publishers Ltd.
• [20] Moingeon P. (2001): Cancer vaccines. — Vaccine, Vol. 19, No. 11–12, pp. 1305–1326.