×

zbMATH — the first resource for mathematics

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.

MSC:
92C50 Medical applications (general)
92C37 Cell biology
34K60 Qualitative investigation and simulation of models involving functional-differential equations
35F20 Nonlinear first-order PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences
45K05 Integro-partial differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.