Autors: Kolev M., Nikolova I., Lazarova, M. D., Stoilova S. Title: A new application of the kinetic type theory in immunology Keywords: Abstract: The kinetic type theory for active particles is a methodology actively used for modeling processes and phenomena in biology and life sciences. One of the fields of its application is immunology, in particular the processes observed in the competition between immune system and foreign antigens. In this paper we present a new mathematical model describing such a complex system and possible occurrence of contemporary diseases. Preliminary qualitative analysis of the model is presented. The role of some of the main model parameters is studied using simulations. References - S. Andrew, C. Baker, G. Bocharov, Rival approaches to mathematical modelling in immunology, Journal of Computational and Applied Mathematics, 205 (2007), 669-686.
- J.F. Bach, Protective role of infections and vaccinations on autoimmune diseases, Journal of Autoimmunity, 16 (2001), 347-353.
- S. Ballantyne, The Paleo Approach: Reverse Auto-immune Disease and Heal your Body, Victory Belt Publishing, Las Vegas, 2013.
- N. Bellomo, Modelling complex living systems, Birkhäuser, Boston, 2008.
- K. Blyuss, L.S. Nicholson, Understanding the roles of activation threshold and infections in the dynamics of autoimmune disease, Journal of Theoretical Biology, 375 (2015), 13-20.
- S. Iwami, Y. Takeuchi, K. Iwamoto, Y. Naruo, M. Yasukawa, A mathematical design of vector vaccine against autoimmune disease, Journal of Theoretical Biology, 256 (2009), 382-392.
- S. Iwami, Y. Takeuchi, Miura, T. Sasaki, T. Kajiwara, Dynamical properties of autoimmune disease models: Tolerance, flare-up, dormancy, Journal of Theoretical Biology, 246 (2007), 646-659.
- C. Janeway, P. Travers, M. Walport, M. Shlomchik, Immunobiology: The Immune System in Health and Disease, Garland Science, New York, 2004.
- M. Kolev, I. Nikolova, On a kinetic type model of autoimmune disease, in Proceedings of the 23rd National Conference on Applicatons of Mathematics in Biology and Medicine, Silesian University of Technology, University of Warsaw, 101-107, 2017.
- K. Leon, J. Faro, A. Lage, J.S. Carneiro, Inverse correlation between the incidences of autoimmune disease and infection predicted by a model of T cell mediated tolerance, Journal of Autoimmunity, 22 (2004), 31-42.
- Marchuk, G. Mathematical modeling of Immune Response in Infections Diseases, Kluwer academic publishers, Dordrecht/Boston/London (1997)
- M. Nowak, R. May, Virus Dynamics, Oxford Univ. Press, Oxford, 2000.
- L. Shampine, M. Reichelt, The Matlab ODE suite, SIAM J. Sci. Comput. 18 (1997), 1-22.
- Stetler-Stevenson, W.G.; Aznavoorian, S.; Liotta, L.A. Tumor cell interactions with the extracellular matrix during invasion and metastasis. Annu. Rev. Cell Biol. 1993, 9, 541-573.
- E. Volkov, Numerical Methods, Hemishere/Mir, New York/Moscow, 1990.
Issue
| Journal of Physics: Conference Series, vol. 2910, pp. 1-9, 2024, United Kingdom, https://doi.org/10.1088/1742-6596/2910/1/012007 |
|