Browse > Article
http://dx.doi.org/10.7858/eamj.2016.014

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)
Publication Information
Abstract
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.
Keywords
IBD model; Immune system; Stability; Sensitivity; Numerical simulation;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 RB. Sartor, Mechanisms of Disease:Pathogenesis of Crohn's Disease and Ulcerative Colitis, Nat Clin Pract Gastroenterol Hepatol. 3, (2006), 390-407.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
11 F. Shanahan, Crohn's disease, The Lancet. 359, (2002), 62-69.   DOI
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.   DOI
13 A.K. Abbas, K.M. Murphy, A. Sher, Functional diversity of helper T lymphocytes, Nature, 383, (1996), 787-793.   DOI
14 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.   DOI
15 L.A. Zenewicz, A. Antov, R.A. Flavell, CD4 T-cell differentiation and inflammatory bowel disease, Trends Mol Med. 15, (2009), 199-207.   DOI