Mathematical modelling of the competition between tumors and immune system considering the role of the antibodies

Mathematical and Computer Modelling

Volumn 37, Issue 11, 2003, Pages 1143-1152

  Kolev, M ^a,b  

^a UNIVERSITY OF WARSAW   (Poland)

^b SOUTH WEST UNIVERSITY NEOFIT RILSKI   (Bulgaria)

Author keywords

Antibodies; Integrodifferential equations; Leukemia; Nonlinear dynamics; Tumor modelling

Indexed keywords

EID: 0038575165     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(03)80018-3     Document Type: Article

References (25)

1. N. Bellomo and G. Forni, Dynamics of tumor interaction with the host immune system, Mathl. Comput. Modelling 20 (1), 107-122, (1994).
2. N. Bellomo, L. Preziosi and G. Forni, On a kinetic (cellular) theory of the competition between tumors and the immune host system, J. Biol. Systems 4, 479-502, (1996).
3. L. Arlotti and M. Lachowicz, Qualitative analysis of a nonlinear integrodifferential equation modelling tumor-host dynamics, Mathl. Comput. Modelling 23 (6), 11-29, (1996).
4. L. Preziosi, From population dynamics to modelling the competition between tumors and immune system, Mathl. Comput. Modelling 23 (6), 135-152, (1996).
5. J.A. Adam and N. Bellomo, Editors, A Survey of Models for Tumor-Immune System Dynamics, Birkhäuser, Boston, MA, (1997).
6. N. Bellomo and E. deAngelis, Strategies of applied mathematics towards an immuno mathematical theory on tumors and immune system interactions, Math. Models Methods Appl. Sci. 8, 1403-1429, (1998).
7. L. Arlotti, A. Gamba and M. Lachowicz, A kinetic model of tumor/immune system cellular interactions, J. Theor. Medicine 4 (1), 39-50, (2002).
8. M. Lachowicz, Competition tumor-immune system, In Proceedings of the Sixth National Conference on Application of Mathematics in Biology and Medicine, Zawoja, September 12-15, pp. 89-93, (2000).
9. B. Firmani, L. Guerri and L. Preziosi, Tumor/immune system competition with medically induced activation/disactivation, Math. Models Methods Appl. Sci. 9, 491-512, (1999).
10. N. Bellomo and M. Lo Schiavo, Lectures Notes on the Mathematical Theory of Generalized Boltzmann Models, World Sci., Singapore, (2000).
11. N. Bellomo and L. Preziosi, Modelling and mathematical problems related to tumor evolution and its interaction with the immune system, Mathl. Comput. Modelling 32 (3/4), 413-452, (2000).
12. L. Arlotti, N. Bellomo and E. de Angells, Generalized kinetic (Boltzmann) models: Mathematical structures and applications, Math. Models Meth. Appl. Sci. 12, 579-604, (2002).
13. M. Lachowicz, From microscopic to macroscopic description for general kinetic models, Math. Models Meth. Appl. Sci. 12, 981-998, (2002).
14. L. Arlotti and N. Bellomo, Population dynamics with stochastic interaction, Transport Theory Statist. Phys. 24 (1-3), 431-443, (1995).
15. L. Arlotti and N. Bellomo, Solution of a new class of nonlinear kinetic models of population dynamics, Appl. Math. Lett. 9 (2), 65-70, (1996).
16. L. Arlotti, N. Bellomo and M. Lachowicz, Kinetic equations modelling population dynamics, Transport Theory Statist. Phys. 29 (1/2), 125-139, (2000).
17. M. Lachowicz and D. Wrzosek, Nonlocal bilinear equations. Equilibrium solutions and diffusive limit, Math. Models Methods Appl. Sci. 11 (8), 1393-1409, (2001).
18. E. Jäger and L. Segel, On the distribution of dominance in a population of interacting anonymous organisms, SIAM J. Appl. Math. 52, 1442-1468, (1992).
19. I.M. Roitt, Essential Immunology, Blackwell Scientific, Oxford, (1991).
20. V.A. Kuznetsov, Basic models of tumor-immune system interactions: Identification, analysis and predictions, In A Survey of Models for Tumor-Immune System Dynamics, (Edited by J.A. Adam and N. Bellomo), pp. 237-294, Birkhäuser, Boston, MA, (1997).
21. F. Calabi and M.S. Neuberger, Editors, Genetics of Immunoglobulin, Elsevier, (1987).
22. W.E. Paul, Editor, Fundamental Immunology, Raven Press, New York, (1984).
23. E. Beutler, M. Lichtman, B. Coller and T. Kipps, Editors, Williams Hematology, McGraw-Hill, (1995).
24. S. Meuer, R. Hussey, J. Hodgdon, T. Hercend, S. Schlossman and E. Reinherz, Lymphocyte mediated lysis, Science 218, 471-473, (1982).
25. M. Kolev, E. Kozłowska and Lachowicz, A mathematical model for leukemia-immune system dynamics, Institute of Applied Mathematics and Mechanics, Warsaw University, (May 2002).