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A contribution to the mathematical modeling of immune-cancer competition Cover

A contribution to the mathematical modeling of immune-cancer competition

Open Access
|Dec 2018

References

  1. 1. D. Hanahan and R. Weinberg, The hallmarks of cancer, Cell, vol. 100, no. 1, pp. 57-70, 2000.10.1016/S0092-8674(00)81683-9
  2. 2. D. Hanahan and R. Weinberg, Hallmarks of cancer: the next generation, Cell, vol. 144, no. 5, pp. 646- 674, 2011.10.1016/j.cell.2011.02.01321376230
  3. 3. A. Bellouquid, E. D. Angelis, and D. Knopoff, From the modeling of the immune hallmarks of cancer to a black swan in biology, Mathematical Models and Methods in Applied Sciences, vol. 23, no. 05, pp. 949-978, 2013.10.1142/S0218202512500650
  4. 4. L. Arlotti, M. Lachowicz, and A. Gamba, A kinetic model of tumor/immune system cellular interaction, Jornal of Theoretical Medicine, vol. 4, no. 1, pp. 39-50, 2002.10.1080/10273660290015170
  5. 5. N. Bellomo, Modeling Complex Living Systems. Birkhäuser, 2008.
  6. 6. N. Bellomo, D. Knopoff, and J. Soler, On the difficult interplay between life, "complexity", and mathematical sciences, Mathematical Models and Methods in Applied Sciences, vol. 23, no. 10, pp. 1861-1913, 2013.10.1142/S021820251350053X
  7. 7. A. Bellouquid and E. D. Angelis, From kinetic models of multicellular growing systems to macroscopic biological tissue models, Nonlinear Analysis: Real World Applications, vol. 12, no. 2, pp. 1111-1122, 2011.10.1016/j.nonrwa.2010.09.005
  8. 8. A. Bellouquid and M. Delitala, Mathematical Modeling of Complex Biological Systems-A Kinetic Theory Approach. Birkhäuser, 2006.
  9. 9. A. Chauviere and I. Brazzoli, On the discrete kinetic theory for active particles. mathematical tools, Mathematical and Computer Modelling, vol. 43, no. 7-8, pp. 933-944, 2006.10.1016/j.mcm.2005.10.001
  10. 10. N. Bellomo, C. Bianca, and M. Mongiovì, On the modeling of nonlinear interactions in large complex systems, Applied Mathematics Letters, vol. 23, no. 11, pp. 1372-1377, 2010.10.1016/j.aml.2010.07.001
  11. 11. I. Brazzoli, E. D. Angelis, and P. E. Jabin, A mathematical model of immune competition related to cancer dynamics, Mathematical Methods in the applied sciences, vol. 33, no. 6, pp. 733-750, 2010.10.1002/mma.1190
  12. 12. N. Bellomo, L. Preziosi, and G. Forni, On a kinetic (cellular) theory for competition between tumors and the host immune systems, Jornal of Biological Systems, vol. 04, no. 04, pp. 479-502, 1996.10.1142/S0218339096000326
  13. 13. N. Bellomo, A. Bellouquid, and M. Delitala, From the mathematical kinetic theory of active particles to multiscale modelling of complex biological systems, Mathematical and Computer Modelling, vol. 47, no. 7-8, pp. 687-698, 2008.10.1016/j.mcm.2007.06.004
  14. 14. S. Farkona, E. P. Diamandis, and I. M. Blasutig, Cancer immunotherapy: the beginning of the end of cancer?, BMC medicine, vol. 14, no. 1, p. 73, 2016.10.1186/s12916-016-0623-5485882827151159
Language: English
Page range: 76 - 90
Submitted on: Jan 16, 2017
Accepted on: Apr 10, 2018
Published on: Dec 19, 2018
Published by: Italian Society for Applied and Industrial Mathemathics
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2018 Najat M. Omar Dabnoun, Maria Stella Mongiovì, published by Italian Society for Applied and Industrial Mathemathics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.