Separable transition density in the hybrid model for tumor-immune system competition

Computational and Mathematical Methods in Medicine

Volumn 2012, Issue , 2012, Pages

  Cattani, Carlo ^a   Ciancio, Armando ^b  

^a UNIVERSITY OF SALERNO   (Italy)

^b UNIVERSITY OF MESSINA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL SYSTEMS; IMMUNE SYSTEM;

CONCRETE APPLICATIONS; EXPLICIT FORM; HYBRID MODEL; LOTKA-VOLTERRA SYSTEMS; TRANSITION DENSITY; TUMOR CELLS;

TUMORS;

ARTICLE; CELL POPULATION; CELL PROLIFERATION; COMPETITION; HYBRID; IMMUNE SYSTEM; LOTKA VOLTERRA EQUATION; MATHEMATICAL PARAMETERS; STOCHASTIC MODEL; TUMOR CELL; TUMOR IMMUNOLOGY; ANIMAL; BIOLOGICAL MODEL; HUMAN; IMMUNOLOGY; NEOPLASM; STATISTICS;

ANIMALS; HUMANS; IMMUNE SYSTEM; MODELS, IMMUNOLOGICAL; NEOPLASMS; STOCHASTIC PROCESSES;

EID: 84856407064     PISSN: 1748670X     EISSN: 17486718     Source Type: Journal    
DOI: 10.1155/2012/610124     Document Type: Article

References (20)

1. Bellomo N., Bellouquid A., Delitala M., Mathematical topics on the modelling complex multicellular systems and tumor immune cells competition Mathematical Models and Methods in Applied Sciences 2004 14 11 1683 1733 (Pubitemid 39526525)
2. Bellomo N., Forni G., Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems Mathematical Models and Methods in Applied Sciences 2006 16 7 1001 1029 (Pubitemid 44076433)
3. Bellomo N., Bellouquid A., On the onset of non-linearity for diffusion models of binary mixtures of biological materials by asymptotic analysis International Journal of Non-Linear Mechanics 2006 41 2 281 293 (Pubitemid 43061445)
4. Bellomo N., Bellouquid A., Nieto J., Soler J., Multicellular biological growing systems: hyperbolic limits towards macroscopic description Mathematical Models and Methods in Applied Sciences 2007 17 1 1675 1692
5. Bellomo N., Delitala M., From the mathematical kinetic, and stochastic game theory to modelling mutations, onset, progression and immune competition of cancer cells Physics of Life Reviews 2008 5 4 183 206
6. Bellomo N., Modeling Complex Living Systems: A Kinetic Theory and Stochastic Game Approach 2008 Boston, Mass, USA Birkhuser
7. Bianca C., Bellomo N., Towards a Mathematical Theory of Multiscale Complex Biological Systems 2010 Singapore World Scientific
8. D'Onofrio A., A general framework for modeling tumor-immune system competition and immunotherapy: mathematical analysis and biomedical inferences Physica D 2005 208 3-4 220 235 (Pubitemid 41085168)
9. d'Onofrio A., Tumor-immune system interaction: modeling the tumor-stimulated proliferation of effectors and immunotherapy Mathematical Models and Methods in Applied Sciences 2006 16 8 1375 1401 (Pubitemid 44221742)
10. d'Onofrio A., Tumor evasion from immune control: strategies of a MISS to become a MASS Chaos, Solitons Fractals 2007 31 2 261 268
11. d'Onofrio A., Metamodeling tumor-immune system interaction, tumor evasion and immunotherapy Mathematical and Computer Modelling 2008 47 5-6 614 637
12. Kuznetsov V. A., Makalkin I. A., Taylor M. A., Perelson A. S., Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis Bulletin of Mathematical Biology 1994 56 2 295 321
13. Stepanova N. V., Course of the immune reaction during the development of a malignant tumour Biophysics 1979 24 5 917 923
14. Tao Y., Zhang H., A parabolic-hyperbolic free boundary problem modelling tumor treatment with virus Mathematical Models and Methods in Applied Sciences 2007 17 1 63 80
15. Kuznetsov V. A., Knott G. D., Modeling tumor regrowth and immunotherapy Mathematical and Computer Modelling 2001 33 12-13 1275 1287 (Pubitemid 32417937)
16. Cattani C., Ciancio A., Lods B., On a mathematical model of immune competition Applied Mathematics Letters 2006 19 7 686 691
17. Cattani C., Ciancio A., Hybrid two scales mathematical tools for active particles modelling complex systems with learning hiding dynamics Mathematical Models and Methods in Applied Sciences 2007 17 2 171 187
18. Cattani C., Ciancio A., Third order model for tumor-immune system competition Proceedings of the 4th International Colloquium Mathematics in Engineering and Numerical Physics 2007 Bucharest, Romania 30 37
19. Cattani C., Ciancio A., Qualitative analysis of second-order models of tumor-immune system competition Mathematical and Computer Modelling 2008 47 11-12 1339 1355 (Pubitemid 351626926)
20. Cattani C., Ciancio A., d'Onofrio A., Metamodeling the learning-hiding competition between tumours and the immune system: a kinematic approach Mathematical and Computer Modelling 2010 52 1-2 62 69