Mathematical insights on psoriasis regulation: Role of Th<sub>1</sub> and Th<sub>2</sub> cells

Amit Kumar Roy; Priti Kumar Roy; Ellina Grigorieva; Amit Kumar Roy; Priti Kumar Roy; Ellina Grigorieva

doi:10.3934/mbe.2018032

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 3: 717-738. doi: 10.3934/mbe.2018032

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Mathematical insights on psoriasis regulation: Role of Th₁ and Th₂ cells

1.
Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata-700032, India
2.
Department of Mathematics and Computer Sciences, Texas Womans University, Denton, TX 76204, USA

Received: 10 April 2017 Revised: 06 July 2017 Published: 01 June 2018
MSC : Primary: 92B05, 97M10; Secondary: 49J15

Psoriasis is an autoimmune disorder, characterized by hyper-proli-feration of Keratinocytes for the abnormal activation of T Cells, Dendritic Cells (DCs) and cytokine signaling. Interaction of DCs and T Cells enable T Cell to differentiate into Type 1 (Th₁), Type 2 (Th₂) helper T Cell depending on cytokine release. Hyper-proliferation of Keratinocytes may occur due to over expression of pro-inflammatory cytokines secreted by Th₁-Cells viz. Interferon gamma ( $\mbox{IFN}-{γ}$ ), Transforming growth factor beta ( $\mbox{TGF}-β$ ) and Tumor necrosis factor alpha ( $\mbox{TNF}-α$ ) etc. Deregulation of epidermal happens due to signaling of anti-inflammatory cytokines like Interleukin 10 ( $\mbox{IL}-{10}$ ), Interleukin 4 ( $\mbox{IL}-{4}$ ) etc., released by Th₂-Cells. In this article, we have constructed a set of nonlinear differential equations involving the above cell population for better understanding the impact of cytokines on Psoriasis. System is analyzed introducing therapeutic agent (Biologic / $\mbox{IL}-{10}$ ) for reducing the hyper-proliferation of Keratinocytes. Effect of Biologic is used as a surrogate of control parameter to reduce the psoriatic lesions. We also studied its effect both in continuous and impulsive dosing method. Our study reveals that impulsive dosing is more applicable compare with continuous dosing to prevent Psoriasis.
- Psoriasis,
- Cytokines,
- Keratinocytes,
- Biologic,
- Optimal control,
- Impulsive approach
Citation: Amit Kumar Roy, Priti Kumar Roy, Ellina Grigorieva. Mathematical insights on psoriasis regulation: Role of Th1 and Th2 cells[J]. Mathematical Biosciences and Engineering, 2018, 15(3): 717-738. doi: 10.3934/mbe.2018032

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Abstract

Psoriasis is an autoimmune disorder, characterized by hyper-proli-feration of Keratinocytes for the abnormal activation of T Cells, Dendritic Cells (DCs) and cytokine signaling. Interaction of DCs and T Cells enable T Cell to differentiate into Type 1 (Th₁), Type 2 (Th₂) helper T Cell depending on cytokine release. Hyper-proliferation of Keratinocytes may occur due to over expression of pro-inflammatory cytokines secreted by Th₁-Cells viz. Interferon gamma ( $\mbox{IFN}-{γ}$ ), Transforming growth factor beta ( $\mbox{TGF}-β$ ) and Tumor necrosis factor alpha ( $\mbox{TNF}-α$ ) etc. Deregulation of epidermal happens due to signaling of anti-inflammatory cytokines like Interleukin 10 ( $\mbox{IL}-{10}$ ), Interleukin 4 ( $\mbox{IL}-{4}$ ) etc., released by Th₂-Cells. In this article, we have constructed a set of nonlinear differential equations involving the above cell population for better understanding the impact of cytokines on Psoriasis. System is analyzed introducing therapeutic agent (Biologic / $\mbox{IL}-{10}$ ) for reducing the hyper-proliferation of Keratinocytes. Effect of Biologic is used as a surrogate of control parameter to reduce the psoriatic lesions. We also studied its effect both in continuous and impulsive dosing method. Our study reveals that impulsive dosing is more applicable compare with continuous dosing to prevent Psoriasis.

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