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A mathematical model of immune competition related to cancer dynamics
Author(s) -
Brazzoli Ilaria,
De Angelis Elena,
Jabin PierreEmmanuel
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1190
Subject(s) - competition (biology) , sort , mathematics , mathematical economics , dynamics (music) , competition model , statistical physics , qualitative analysis , calculus (dental) , ecology , physics , neoclassical economics , sociology , economics , biology , qualitative research , profit (economics) , social science , medicine , arithmetic , dentistry , acoustics
This paper deals with the qualitative analysis of a model describing the competition among cell populations, each of them expressing a peculiar cooperating and organizing behavior. The mathematical framework in which the model has been developed is the kinetic theory for active particles. The main result of this paper is concerned with the analysis of the asymptotic behavior of the solutions. We prove that, if we are in the case when the only equilibrium solution if the trivial one, the system evolves in such a way that the immune system, after being activated, goes back toward a physiological situation while the tumor cells evolve as a sort of progressing travelling waves characterizing a typical equilibrium/latent situation. Copyright © 2009 John Wiley & Sons, Ltd.