A mathematical model of immune competition related to cancer dynamics

作者：Brazzoli Ilaria; De Angelis Elena^*; Jabin Pierre Emmanuel

来源：Mathematical Methods in the Applied Sciences, 2010, 33(6): 733-750.

DOI：10.1002/mma.1190

• kinetic theory for active particles
• Cauchy problem
• travelling waves
• complex systems
• biological systems
• cell population
• tumor-immune competition
• tumor dormancy

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.

• 出版日期2010-4