Dinamika Model Matematika Reaksi T-Helper

Chilvia Tribhuana, Usman Pagalay, Elly Susanti


T cells are a major component of the human immune system. These T cells have a number that varies depending on the body's immune response when fighting bacteria or viruses. However, the condition of excess immune cells in the body can also be dangerous. Theoretical studies on the dynamics of T-Helper cells in the body are needed to get the right simulation in treating patients without conducting medical tests on every patient on a daily basis. This study discusses the dynamics of the mathematical model of the T-Helper reaction with the influence of antigen and IL-2. From this study, two equilibrium points were obtained, namely disease-free equilibrium and endemic equilibrium. The use of parameter values from the experimental results shows that the disease-free equilibrium point is locally unstable, while the endemic equilibrium point is locally stable. The numerical simulation showed that the antigen increased from 1st day to the highest value at 0.926 on the 11th day until on the 20th day it started to be constant towards at the value  which is the antigen could be activate the resting T-Helper. The process of activating T-Helper, create IL-2 which can stimulating the proliferation and activity of T-Helper cells, so they can divide the activated cell of T-Helper into two memory cells.


T-Helper; Dynamics Mathematical Model; Equilibrium Point; Stability Analysis; Routh Hurwitz

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A. R. Pratiwi and dkk, Pangan Untuk Sistem Imun, M. Hasdar and dkk, Eds., SCU Knowledge Media, 2020, p. 57.

S. N. Aidah, Sistem Imun Manusia, PENERBIT KBM INDONESIA, 2020, p. 90.

L. B. Togatorop, H. Mawarti, B. A. Saputra and dkk, Keperawatan Sistem Imun dan Hematologi, A. Karim, Ed., Yayasan Kita Menulis, 2021, p. 232.

I. Kerpan, Sel T, Cambridge Stanford Books.

Syarifuddin, Imunologi Dasar Prinsip Dasar Sistem Kekebalan Tubuh, Cendekia Publisher, 2019, p. 120.

C. V. Rao, Textbook of Immunology, Alpha Science International, Limited, 2019, p. 436.

L. Schmitz, B. Berdien, E. Huland and dkk, "The Impact of a New Interleukin-2-Based Immunotherapy Candidate on Urothelial Cells to Support Use for Intravesical Drug Delivery," Journal Life, pp. 1-17, 2020.

M. F. Bachmann and A. Oxenius, "Interleukin 2: From Immunostimulation to Immunoregulation and Back Again," Eurpean Molecular Biology Organization, pp. 1142-1148, 2007.

A. R. McLean, "Modelling T Cell Memory," Academic Press Limited, pp. 63-74, 1994.

A. R. McLean and T. B. L. Kirkwood, "A Model of Human Immunodeficiency Virus Infection in T Helper Cell Clones," J. theor. Biol, pp. 177-203, 1990.

K. A. Smith, "Interleukin-2: Inception, Impact, and Implications," Science 240, pp. 1169-1176, 1988.

K. A. Smith and D. A. Cantrell, "Interleukin 2 Regulates its Own Receptors," Proc. nain. Acad. Sci. U.S.A., pp. 864-868, 1985.

D. A. Cantrell and K. A. Smith, "Transient Expression of Interleukin 2 Receptors Consequences for T Cell Growth," J. epl Med. 158, pp. 1895-1911, 1983.

D. C. Male and A. Cooke, Advanced Immunology, London: London: Gower Medical Publishing, 1987.

D. Gray and P. Matzinger, "T Cell Memory is Short-Lived In the Absence of Antigen," J. expl Med. 174, pp. 969-974, 1991.

DOI: https://doi.org/10.18860/jrmm.v1i5.14477


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