[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.7858/eamj.2022.023

THE IMPACT OF DELAY IN THE TREATMENT OF AUTOINFLAMMATORY DISEASE WITH A MATHEMATICAL MODEL

Park, Anna (Department of Mathematics, Pusan National University)

Publication Information

East Asian mathematical journal / v.38, no.3, 2022 , pp. 357-363 More about this Journal

Abstract

Immunological imbalance eventually results in the development of various diseases. A typical example is an imbalance of cytokines with immunomodulatory abilities. In this paper, we propose a two-variable delay model to anti-pro-inflammatory cytokine therapy for autoimmune diseases, which are caused by an imbalance between the pro and anti-inflammatory cytokines. The interaction between pro- and anti-inflammatory cytokines were modeled mathematically to investigate the relevance of cytokines in disease processes. The delay time was estimated to maintain the stability of a biologically important steady state. In particular, the effects of delay with anti-pro-inflammatory cytokines therapy in autoinflammatory diseases were studied.

Keywords

Mathematical model; Delay differential equation; Autoinflammatory disease; Stability analysis;

Citations & Related Records

Reference

1	Greenwald, R.J., G.J. Freeman, and A.H. Sharpe, THE B7 F AMILY REVISITED. Annual Review of Immunology, 23(1): 515-548, 2005. DOI
2	Romagnani, Sergio. "Immunological tolerance and autoimmunity." Internal and emergency medicine 1.3 (2006): 187-196. DOI
3	Goodnow, Christopher C. "Balancing immunity and tolerance: deleting and tuning lymphocyte repertoires." Proceedings of the National Academy of Sciences 93.6 (1996): 2264-2271. DOI
4	Bouma, G. and W. Strober, The immunological and genetic basis of inflammatory bowel disease. Nat Rev Immunol, 3(7): 521, 2003. DOI
5	O'Shea, John J., Averil Ma, and Peter Lipsky. "Cytokines and autoimmunity." Nature Reviews Immunology 2.1 (2002): 37-45. DOI
6	Baker, Michelle, et al. "Mathematical modelling of cytokine-mediated inflammation in rheumatoid arthritis." Mathematical medicine and biology: a journal of the IMA 30.4 (2013): 311-337. DOI
7	Seymour, R. M. & Henderson, B. (2001) Pro-inflammatoryanti-inflammatory cytokine dynamics mediated by cytokine-receptor dynamics in monocytes. Math. Med. Biol., 18, 159192.
8	H. Nyquist, Regeneration theory, Bell Syst. Tech. J. 11 (1) (1932) 126147. DOI
9	Jit, M., Henderson, B., Stevens, M. & Seymour, R. M. (2005) TNF neutralization in cytokine-driven dis- eases: a mathematical model to account for therapeutic success in rheumatoid arthritis but therapeutic failure in systemic inflammatory response syndrome. Rheumatology, 44, 323331.
10	Goronzy, Jrg J., and Cornelia M. Weyand. "Developments in the scientific understanding of rheumatoid arthritis." Arthritis research & therapy 11.5 (2009): 1-14.
11	Homey, B., et al., Cytokines and chemokines orchestrate atopic skin inflammation. Journal of Allergy and Clinical Immunology, 118(1): 178-189, 2006. DOI
12	Hogquist, K.A., T.A. Baldwin, and S.C. Jameson, Central tolerance: learning self-control in the thymus. Nat Rev Immunol, 5(10): 772, 2005 DOI
13	H.I. Freedman, L. Erbe, V.S.H. Rao, Three species food chain models with mutual interference and time delays, Math. Biosci. 80 (1) (1986) 5780.