East Asian mathematical journal

  • 제32권1호
  • /
  • Pages.139-152
  • /
  • 2016
  • /
  • 1226-6973(pISSN)
  • /
  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

A MATHEMATICAL MODEL OF IMMUNE-MEDIATED DISORDER IN INFLAMMATORY BOWEL DISEASE

  • Park, Anna (Department of Mathematics, Pusan National University) ;
  • Jung, Il Hyo (Department of Mathematics, Pusan National University)
  • 투고 : 2016.01.02
  • 심사 : 2016.01.30
  • 발행 : 2016.01.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Inflammatory Bowel Disease(IBD) is chronic, relapsing, immune mediated disorder. The exact cause of IBD is still unknown. The immune system is known to play important role in the dynamics of IBD. We focus on relation between T cells and cytokines in immune system that leads to IBD. In this paper, we propose a mathematical model describing IBD under considering immune mediated disorder by using ordinary differential equations. The existence and stability of the model are established, where an applicable basin of attraction are calculated and examined. Some numerical simulations are presented to verify the proposed results and as changing parameter values given by sensitivity analysis, we show how to change dynamic behaviors of the model.

키워드

참고문헌

  1. RB. Sartor, Mechanisms of Disease:Pathogenesis of Crohn's Disease and Ulcerative Colitis, Nat Clin Pract Gastroenterol Hepatol. 3, (2006), 390-407. https://doi.org/10.1038/ncpgasthep0528
  2. B.I. Jang, S.H. Lee, Update in the Pathogenesis of Inflammatory Bowel Disease, J.Kor.Soc.Colo. 24, (2008), 302-309.
  3. V. Andersen, A. Olsen, F. Carbonnel, A. Tjnneland, U. Vogel, Diet and risk of inflammatory bowel disease, Dig Liver Dis. 44, (2012), 185-194. https://doi.org/10.1016/j.dld.2011.10.001
  4. A.K. Abbas and A.H. Lichtman, Cellular and Molecular Immunology, 7th ed., Elsevier Saunders, St. Louis, MO, 2011.
  5. P.K. Roy, J. Bhadra, B. Chattopadhyay, Chattopadhyay Mathematical Modeling on Immunopathogenesis in Chronic Plaque of Psoriasis: A Theoretical Study, Lecture Notes in Engineering and Computer Science, WCE, UK, (2010), Vol. 1, 550-555.
  6. Helen Moorea, Natasha K. Lib, A mathematical model for chronic myelogenous leukemia(CML) and T cell interaction, J Theor Biol. 227, (2004) 513-523. https://doi.org/10.1016/j.jtbi.2003.11.024
  7. M. Baker, S. Denman-Johnson, B.S. Brook, I. Gaywood, M.R. Owen., Mathematical modelling of cytokine-mediated inflammation in rheumatoid arthritis, Math Med Biol. 30 (2012), 1-27.
  8. R.M Seymour, B. Henderson, Pro-inflammatory.anti-inflammatory cytokine dynamics mediated by cytokine-receptor dynamics in monocytes, Math Med Biol. 18, (2001), 159-192. https://doi.org/10.1093/imammb/18.2.159
  9. K. Wendelsdorf, J. Bassaganya-Riera, R. Hontecillas, S. Eubank, Model of colonic inflammation : Immune modulatory mechanisms in in ammatory bowel disease, J Theor Biol. 264, (2010), 1225-1239. https://doi.org/10.1016/j.jtbi.2010.03.027
  10. W.-C.Lo, R.I.Arsenescu, A.Friedman, Mathematical model of the roles of T cells in inflammatory bowel disease, Bull Math Biol. 75, (2013), 1417-33. https://doi.org/10.1007/s11538-013-9853-2
  11. F. Shanahan, Crohn's disease, The Lancet. 359, (2002), 62-69. https://doi.org/10.1016/S0140-6736(02)07284-7
  12. P. Romagnani, F. Annunziato, M.C Baccari and P. Parronchi., T cells and cytokines in Crohn's disease, Curr Opin Immunol. 9, (1997), 793-799. https://doi.org/10.1016/S0952-7915(97)80180-X
  13. A.K. Abbas, K.M. Murphy, A. Sher, Functional diversity of helper T lymphocytes, Nature, 383, (1996), 787-793. https://doi.org/10.1038/383787a0
  14. L.A. Zenewicz, A. Antov, R.A. Flavell, CD4 T-cell differentiation and inflammatory bowel disease, Trends Mol Med. 15, (2009), 199-207. https://doi.org/10.1016/j.molmed.2009.03.002
  15. Y. Kogan, Z. Agur and M. Elishmereni, A mathematical model for the immunotherapeutic control of the Th1/Th2 imbalance in melanoma, DCDS-B, 18, (2013), 1017-1030. https://doi.org/10.3934/dcdsb.2013.18.1017