Abstract
Lymphocytes play significant defensive role to keep the body healthy. However, there is substantial evidence that adrenal hormones such as epinephrine, norepinephrine, and cortisol generated by psychological stress suppress the activities of the immune system or alter the activation and mobilization several immune cells particularly lymphocytes during infections. Glucocorticoid receptors expressed by the immune cells makes binding those hormones possible. This work formulates a mathematical model to examine the impact of adrenal hormones on the immune system with respect to time evolution and spatial distribution cells in response to hormones concentration. The steady state of the model is studied and found to be uniformly and asymptotically stable subject to the secretion and decay rates of hormones. The numerical experiments using the free diffusion equations further investigates the dynamic behaviour of the “bound” lymphocytes secretion rate of the adrenal hormones induced by psychological stress.
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References
Phetlhu, D.R., Watson, M.: Challenges faced by grandparents caring for AIDS orphans in Koster, North West Province of South Africa. Afr. J. Phys. Health Educ. Recreat. Dance (Supp 1:2), 348–359 (2014)
Benjamini, E., Coico, R., Sunshine, G.: Immunology: A Short Course, 4th edn. Wiley-Liss, New York (2000)
Rabin, B.S.: Stress, Immune Function, and Health: The Connection. Wiley, New York (1999)
Middleton, D., Curran, M., Maxwell, L.: Natural killer cells and their receptors. Transpl. Immunol. 10(2–3), 147–164 (2002)
Rajalingam, R.: Overview of the killer cell immunoglobulin-like receptor system. Methods Mol. Biol. 882, 391–414 (1999)
Tenibiaje, D.J.: Counselling Psychology. Esthom Graphic Prints, Ibadan (2011)
Felten, S.Y., Felten, D.: Neural-immune interaction. Prog. Brain Res. 100, 157–162 (1994). PubMed
Ferguson, R.G., et al.: Immune parameters in a longitudinal study of a very old population of Swedish people: a comparison between survivors and nonsurvivors. J. Gerontol. A Biol. Sci. Med. Sci. 50, B378–B382 (1995)
Patterson, S., et al.: Cortisol patterns are associated with T cell activation in HIV. PLoS ONE 8(7), e63429 (2013)
Samuel, S., Gill, V.: Diffusion-chemotaxis model of effects of cortisol on immune response to human immunodeficiency virus. Nonlinear Eng. 7(3), 207–227 (2018)
Mai, M., Wang, K., Huber, G., Kirby, M., Shattuck, M.D., O’Hern, C.S.: Outcome prediction in mathematical models of immune response to infection. PLoS ONE 10, e0135861 (2015)
Hogue, I.B., Bajaria, S.H., Fallert, B.A., Qin, S., Reinhart, T.A., et al.: The dual role of dendritic cells in the immune response to human immunodeficiency virus type 1 infection. J. Gen. Virol. 89, 2228–2239 (2008)
Okada, T., Miller, M.J., Parker, I., et al.: Antigen-engaged B cells undergo chemotaxis toward the T zone and form motile conjugates with helper T cells. PLoS Biol. 3(6), 1047–1061 (2005)
Grimshaw, R.: Nonlinear Ordinary Differential Equations, pp. 23–44. Pi-Square Press, Nottingham (1990)
Boyer, F., Fabrie, P.: Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related Models, vol. 183. Springer Science & Business Media (2012)
Süli, E., Mayers, D.: An Introduction to Numerical Analysis. Cambridge University Press (2003)
John, C.T., Dale, A., Richard, H.P.: Computational Fluid Mechanics and Heat Transfer, 2nd edn. Taylor & Francis (1997)
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Samuel, S., Gill, V., Kumar, D., Singh, Y. (2019). Numerical Study of Effects of Adrenal Hormones on Lymphocytes. In: Singh, J., Kumar, D., Dutta, H., Baleanu, D., Purohit, S. (eds) Mathematical Modelling, Applied Analysis and Computation. ICMMAAC 2018. Springer Proceedings in Mathematics & Statistics, vol 272. Springer, Singapore. https://doi.org/10.1007/978-981-13-9608-3_18
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DOI: https://doi.org/10.1007/978-981-13-9608-3_18
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