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These analytical results generalize the earlier findings, which were obtained for a trilinear reaction rate (which corresponds to the law of mass action) and reported in [18,19], to the case of a general rate of reaction. These results allow to reduce the problem of constructing the optimal control to a straightforward constrained finite dimensional optimization problem.

*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 (Th_{1}), Type 2 (Th_{2}) helper T Cell depending on cytokine release. Hyper-proliferation of Keratinocytes may occur due to over expression of pro-inflammatory cytokines secreted by Th_{1}-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 Th_{2}-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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