On the modelling of genetic mutations and immune system competition

Computers and Mathematics with Applications

Volumn 61, Issue 9, 2011, Pages 2362-2375

  Bianca, C ^a   Delitala, M ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

Biology; Immune system; Kinetic theory; Living systems; Nonlinearity

Indexed keywords

ACTIVE PARTICLES; CANCER PROGRESSION; CELLULAR SYSTEM; EVOLUTIONARY DYNAMICS; GENETIC MUTATIONS; IMMUNE SYSTEM CELLS; IMMUNE SYSTEMS; LIVING SYSTEMS; NON-LINEARITY; NUMERICAL SIMULATION; SELECTIVE PRESSURE;

BIOLOGICAL SYSTEMS; COMPETITION; COMPUTER SIMULATION; DISEASES; DISPLAY DEVICES; IMMUNOLOGY; KINETIC THEORY;

MATHEMATICAL MODELS;

EID: 79955466552     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2011.01.024     Document Type: Article

References (43)

1. J.D. Watson, and F.H. Crick Molecular structure of nucleic acids: a structure for deoxyribose nucleic acid Nature 171 1953 737 738
2. D. Hanahan, and R.A. Weinberg The hallmarks of cancer Cell 100 2000 57 70 (Pubitemid 30046295)
3. V. Cristini, and J. Lowengrub Multiscale Modeling of Cancer. An Integrated Experimental and Mathematical Modeling Approach 2010 Cambridge University Press
4. N. Bellomo, and M. Delitala From the mathematical kinetic, and stochastic game theory to modelling mutations, onset, progression and immune competition of cancer cells Physics of Life Reviews 5 2008 183 206
5. N. Bellomo, N.K. Li, and P.K. Maini On the foundations of cancer modelling: selected topics, speculations, & perspectives Math. Models Methods Appl. Sci. 18 2008 593 646 (Pubitemid 351730142)
6. M.L. Martins, S.C Ferreira Jr., and M.J. Vilela Multiscale models for the growth of avascular tumors Physics of Life Reviews 4 2007 128 156
7. N. Bellomo, C. Bianca, and M. Delitala Complexity analysis and mathematical tools towards the modelling of living systems Physics of Life Reviews 6 2009 144 175
8. F. Schweitzer Brownian Agents and Active Particles 2003 Springer Berlin
9. N. Bellomo, and G. Forni Complex multicellular systems and immune competition: new paradigms looking for a mathematical theory Current Topics in Developmental Biology 81 2008 485 502
10. R. Reed Why is mathematical biology so hard? Notices Amer. Math. Soc. 51 2004 338 342
11. H.L. Hartwell, J.J. Hopfield, S. Leibner, and A.W. Murray From molecular to modular cell biology Nature 402 1999 c47 c52
12. M. Nowak Evolutionary Dynamics: Exploring the Equations of Life 2006 Belknap Press
13. N. Bellomo, L. Preziosi, and G. Forni On a kinetic (cellular) theory for competition between tumors and the host immune system J. Biological Systems 4 1996 479 502 (Pubitemid 126491070)
14. A. Bellouquid, and M. Delitala Mathematical Modeling of Complex Biological Systems: A Kinetic Theory Approach 2006 Birkuser Boston
15. L. Arlotti, A. Gamba, and M. Lachowicz A kinetic model of tumor/immune system cellular interactions J. Theoret. Med. 4 2002 39 50 (Pubitemid 34506360)
16. A. Bellouquid, and M. Delitala Mathematical models and tools of kinetic theory toward modelling complex biological systems Math. Models Methods Appl. Sci. 15 2005 1639 1666 (Pubitemid 41551041)
17. M. Kolev Mathematical modeling of the competition between acquired immunity and cancer Int. J. Appl. Math. Comput. Sci. 13 2003 289 296
18. M. Kolev Mathematical modelling of the competition between tumors and immune system considering the role of antibodies Math. Comput. Modelling 37 2003 1143 1152 (Pubitemid 36761621)
19. M. Kolev, E. Kozlowska, and M. Lachowicz A mathematical model for single cell cancer Immune system dynamics Math. Comput. Modelling 41 2005 1083 1095 (Pubitemid 41444865)
20. E. De Angelis, and P.E. Jabin Qualitative analysis of a mean field model of tumor-immune system competition Math. Models Methods Appl. Sci. 13 2003 187 206 (Pubitemid 36344999)
21. E. De Angelis, and P.E. Jabin Mathematical models of therapeutical actions related to tumour and immune system competition Math. Methods Appl. Sci. 28 2005 2061 2083 (Pubitemid 41625301)
22. L.D. Greller, F.L. Tobin, and G. Poste Tumor heterogeneity and progression: conceptual foundations for modeling Invasion Metastasis 16 1996 177 208 (Pubitemid 27399786)
23. P.C. Nowell Tumor progression: a brief historical perspective Seminars in Cancer Biology 12 2002 261 266 (Pubitemid 35034570)
24. L.G. De Pillis, W. Gu, and A.E. Radunskaya Mixed immunotherapy and chemotherapy of tumors: modeling applications and biological interpretations J. Theoret. Biol. 238 2006 841 862 (Pubitemid 43175834)
25. A. D'Onofrio Tumor-immune system interaction: modeling the tumor-stimulated proliferation of effectors and immunotherapy Math. Models Methods Appl. Sci. 16 2006 1375 1401 (Pubitemid 44221742)
26. G.P. Dunn, A.Y. Bruce, H. Ikeda, L.J. Old, and R.D. Schreiber Cancer immunoediting: from immunosurveillance to tumor escape Nature Immunology 3 2002 991 998 (Pubitemid 35363648)
27. P. Friendl, A.T. De Boer, and M. Gunzer Tuning immune responses: diversity and adaptation of the immunological synapse Nature Reviews Immunology 5 2005 532 545 (Pubitemid 40961331)
28. M.A.J. Chaplain Modelling aspects of cancer growth: insight from mathematical and numerical analysis and computational simulation Multiscale Problems in the Life Sciences. From Microscopic to Macroscopic Lecture Notes in Mathematics 2008 Springer Heidelberg 147 200
29. P.L. Lollini, S. Motta, and F. Pappalardo Modelling tumor immunology Math. Models Methods Appl. Sci. 16 2006 1091 1124
30. R.A. Gatenby, R.J. Gillies, and J.S. Brown The evolutionary dynamics of cancer prevention Nature Reviews Cancer 10 2010 526 527
31. A.R. Anderson, A.M. Weaver, P.T. Cummings, and V. Quaranta Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment Cell 127 2006 905 915 (Pubitemid 44792251)
32. S. De Lillo, M. Delitala, and M.C. Salvatori Modelling epidemics and virus mutations by methods of the mathematical kinetic theory for active particles Math. Models Methods Appl. Sci. 19 2009 1405 1425
33. C. Bianca Mathematical modelling for keloid formation triggered by virus: Malignant effects and immune system competition Math. Models Methods Appl. Sci. 21 2011 10.1142/S021820251100509X
34. R.A. Weinberg The biology of cancer Garland Sciences 2007 Taylor and Francis Group New York
35. C. Bianca On the modelling of space dynamics in the kinetic theory for active particles Math. Comput. Modelling 51 2010 72 83
36. E.W. Thompson, and D.F. Newgreen Carcinoma invasion and metastasis: a role for epithelialmesenchymal transition? Cancer Res. 65 2005 5991 5995 (Pubitemid 40994377)
37. L. Lund, and K.L. Bowers Sinc Methods for Quadrature and Differential Equations 1987 Society for Industrial Mathematics
38. N. Bellomo, and L. Ridolfi Solution of nonlinear initial-boundary value problems by Sinc collocation-interpolation methods Comput. Math. Appl. 29 1995 15 28
39. N. Bellomo, and M. Delitala On the coupling of higher and lower scales using the mathematical kinetic theory of active particles Appl. Math. Lett. 22 2009 646 650
40. E. Gabetta, and E. Ragazzini About the gene families size diustribution in a recent model of genome evolution Math. Models Methods Appl. Sci. 20 2010 1005 1020
41. J. Paulsson Models of stochastic gene expression Physics of Life Reviews 2 2005 157 175 (Pubitemid 40792434)
42. J. Tiuryn, D. Wojtowicz, and R. Rudnicki A discrete model of evolution of small paralog families Math. Models Methods Appl. Sci. 17 2007 933 955
43. N. Bellomo, A. Bellouquid, J. Nieto, and J. Soler Multiscale biological tissue models and flux-limited chemotaxis for multicellular growing systems Math. Models Methods Appl. Sci. 20 2010 1179 1207