Mathematical methods and tools of kinetic theory towards modelling complex biological systems

Mathematical Models and Methods in Applied Sciences

Volumn 15, Issue 11, 2005, Pages 1639-1666

  Bellouquid, Abdelghani ^a   Delitala, Marcello ^b  

^a National School of Applied Sciences   (Morocco)

^b POLITECNICO DI TORINO   (Italy)

Author keywords

Kinetic theory; Nonlinearity; Population models; Statistical mechanics

Indexed keywords

EID: 27644478289     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202505000923     Document Type: Article

References (18)

1. Eds. J. Adam and N. Bellomo, A Survey of Models on Tumor Immune Systems Dynamics (Birkhäuser, 1997).
2. L. Arlotti, N. Bellomo and E. De Angelis, Generalized kinetic (Boltzmann) models: Mathematical structures and applications, Math. Mod. Meth. Appl. Sci. 12 (2002) 579-604.
3. L. Arlotti, L. Bellomo, E. De Angelis and M. Lachowicz, Generalized Kinetic Models in Applied Sciences - Lecture Notes on Mathematical Problems (World Scientific, 2003).
4. L. Arlotti, M. Lachowicz and A. Gamba, A kinetic model of tumor/immune system cellular interactions, J. Theor. Med. 4 (2002) 39-50.
5. N. Bellomo, A. Bellouquid and M. Delitala, Mathematical topics in the modelling complex multicellular systems and tumor immune cells competition, Math. Mod. Meth. Appl. Sci. 14 (2004) 1683-1733.
6. A. Bellouquid and M. Delitala, Kinetic (cellular) models of cell progression and competition with the immune system, Z. Agnew. Math. Phys. 55 (2004) 295-317.
7. A. Bellouquid and M. Delitala, On the asymptotic behavior of the solution to the Cauchy problem for a model of complex biological systems, submitted (2004).
8. N. Bellomo and G. Forni, Dynamics of tumor interaction with the host immune system, Math. Comp. Model. 20 (1994) 107-122.
9. N. Bellomo and G. Forni, New paradigms towards a biological-mathematical theory of complex multicellular systems, Math. Mod. Meth. Appl. Sci., to appear.
10. Eds. N. Bellomo and M. Pulvirenti, Modelling in Applied Sciences: A Kinetic Theory Approach (Birkhäuser, 2000).
11. M. L. Bertotti and M. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Math. Mod. Meth. Appl. Sci. 14 (2004) 1061-1084.
12. C. Cercignani, R. Illner and M. Pulvirenti, Theory and Application of the Boltzmann Equation (Springer, 1993).
13. L. Derbel, Analysis of a new model for tumor-immune system competition including long time scale effects, Math. Mod. Meth. Appl. Sci. 14 (2004) 1657-1682.
14. E. De Angelis and P. E. Jabin, Qualitative analysis of a mean field model of tumor-immune system competition, Math. Mod. Meth. Appl. Sci. 13 (2003) 187-206.
15. L. Greller, F. Tobin and G. Poste, Tumor hetereogenity and progression: Conceptual foundation for modelling, Invasion Metastasis 16 (1996) 177-208.
16. H. L. Hartwell, J. J. Hopfield, S. Leibner and A. W. Murray, From molecular to modular cell biology, Nature 402 (1999) c47-c52.
17. M. Kolev, Mathematical modelling of the competition between tumors and immune system considering the role of antibodies, Math. Comp. Model. 37 (2003) 1143-1152.
18. L. Preziosi, Modelling Cancer Growth (CRC Press, 2003).