J. Nonl. Evol. Equ. Appl. 2013 (3), pp. 23-42, published on March 13, 2013:

Impact of Cytokine Release in Psoriasis: A Control Based Mathematical Approach

P. K. Roy, A. Datta

Center for Mathematical Biology and Ecology,
Department of Mathematics, Jadavpur University, Kolkata - 700032, India.

Received on January 14, 2012, Revised version: March 5, 2012
Accepted on March 5, 2012

Communicated by Gaston M. N'Guérékata

Abstract.  Psoriasis is a frequent unremitting chronic autoimmune skin ailment, illustrated by T-Cells arbitrated hyperproliferation of Keratinocytes. It was also scrutinized that, psoriatic lesions are sharply demarcated, red and to some extent raised lesions along with silver whitish scales. This category of skin disorder is distinguished by macroscopic and microscopic skin adaptations. In this paper, we consider a mathematical model of Psoriasis, involving T-Cells, Dendritic Cells and epidermal Keratinocytes. After stimulation, the little polypeptides, secreted by abundant cells, are identified as Cytokines, which are also regarded as local hormones of immune organization.

Here we integrate the new idea, i.e., effect of Cytokines release in our proposed model. Our analytical and numerical results reveal that, due to control effect, drug effort impedes the interaction between T-Cells and Keratinocytes by suppressing the Cytokines release to restrict Psoriasis and if the activation rate of Keratinocytes by T-Cells mediated Cytokines can be controlled, then Keratinocytes intensity is stabilized in the plaque of psoriatic pathogenesis.

Keywords: T-Cells, Dendritic Cells, Keratinocytes, Cytokine Release, Drug Efficacy, Optimal Control.
2010 Mathematics Subject Classification:   37N25, 37N35, 37N40, 92B05, 92C50.

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