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On a mathematical model of immune competition. (English) Zbl 1278.92017
Summary: This work deals with the qualitative analysis of a nonlinear integro-differential model of immune competition with special attention to the dynamics of tumor cells contrasted by the immune system. The analysis gives evidence of how initial conditions and parameters influence the asymptotic behavior of the solutions.

92C50Medical applications of mathematical biology
92C37Cell biology
34K60Qualitative investigation and simulation of models
35F20General theory of first order nonlinear PDE
35Q92PDEs in connection with biology and other natural sciences
45K05Integro-partial differential equations
Full Text: DOI
[1] Bellouquid, A.; Delitala, M.: Kinetic (Cellular) approach to models of cell progression and competition with the immune system. Z. angew. Math. phys. 55, 295-317 (2004) · Zbl 1047.92022
[2] Bellouquid, A.; Delitala, M.: Mathematical methods and tools of kinetic theory towards modelling complex biological systems. Math. models methods appl. Sci. 15 (2005) · Zbl 1093.82016
[3] Arlotti, L.; Bellomo, N.; De Angelis, E.: Generalized kinetic (Boltzmann) models: mathematical structures and applications. Math. models methods appl. Sci. 12, 579-604 (2002) · Zbl 1174.82325
[4] Bellomo, N.; Bellouquid, A.; Delitala, M.: Mathematical topics on the modelling complex multicellular systems and tumor immune cells competition. Math. models methods appl. Sci. 14, 1683-1733 (2004) · Zbl 1060.92029
[5] Bellomo, N.; Forni, G.: Dynamics of tumor interaction with the host immune system. Math. comput. Modelling 20, 107-122 (1994) · Zbl 0811.92014
[6] Nowell, P. C.: Tumor progression: a brief historic perspective. Semin. cancer biol. 12, 261-266 (2002)
[7] Delves, P. J.; Roitt, Y. M.: The immune system. Adv. immunol. 343, 37-49 (2000)