Mathematical insights on psoriasis regulation: Role of Th1 and Th2 cells
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 c...
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AIMS Press
2018-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2018032 |
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| author | Amit Kumar Roy Priti Kumar Roy Ellina Grigorieva |
| author_facet | Amit Kumar Roy Priti Kumar Roy Ellina Grigorieva |
| author_sort | Amit Kumar Roy |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c597b55a47274cc6bdd0fc028202f2e3 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2018-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-c597b55a47274cc6bdd0fc028202f2e32025-01-24T02:40:50ZengAIMS PressMathematical Biosciences and Engineering1551-00182018-05-0115371773810.3934/mbe.2018032Mathematical insights on psoriasis regulation: Role of Th1 and Th2 cellsAmit Kumar Roy0Priti Kumar Roy1Ellina Grigorieva2Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata-700032, IndiaCentre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata-700032, IndiaDepartment of Mathematics and Computer Sciences, Texas Womans University, Denton, TX 76204, USAPsoriasis 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.https://www.aimspress.com/article/doi/10.3934/mbe.2018032psoriasiscytokineskeratinocytesbiologicoptimal controlimpulsive approach |
| spellingShingle | Amit Kumar Roy Priti Kumar Roy Ellina Grigorieva Mathematical insights on psoriasis regulation: Role of Th1 and Th2 cells Mathematical Biosciences and Engineering psoriasis cytokines keratinocytes biologic optimal control impulsive approach |
| title | Mathematical insights on psoriasis regulation: Role of Th1 and Th2 cells |
| title_full | Mathematical insights on psoriasis regulation: Role of Th1 and Th2 cells |
| title_fullStr | Mathematical insights on psoriasis regulation: Role of Th1 and Th2 cells |
| title_full_unstemmed | Mathematical insights on psoriasis regulation: Role of Th1 and Th2 cells |
| title_short | Mathematical insights on psoriasis regulation: Role of Th1 and Th2 cells |
| title_sort | mathematical insights on psoriasis regulation role of th1 and th2 cells |
| topic | psoriasis cytokines keratinocytes biologic optimal control impulsive approach |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2018032 |
| work_keys_str_mv | AT amitkumarroy mathematicalinsightsonpsoriasisregulationroleofth1andth2cells AT pritikumarroy mathematicalinsightsonpsoriasisregulationroleofth1andth2cells AT ellinagrigorieva mathematicalinsightsonpsoriasisregulationroleofth1andth2cells |