Saturation Effects on Immunopathogenic Mechanism of Psoriasis:A theoretical approach

Psoriasis vulgaris is a common chronic autoimmune inflammatory skin disease characterized by T-cell mediated hyper proliferation of keratinocytes.This type of skin disorder is characterized by macroscopic and also microscopic skin alterations.It was observed that,psoriatic lesions are sharply demarcated,red and slightly raised lesions along with silver whitish scales.The striking feature of T-cell mediated chronic psoriatic lesions are the epidermal infiltration of predominantly oligoclonal CD8+T-cells and probably also of CD4+T-cells in the dermis.In this research article we proposed a mathematical model for the chronic disease,psoriasis,consisting a set of differential equations,involving T-Lymphocytes cells,Dendritic cells and the epidermal Keratinocytes,incorporating half saturation constant through the T lymphocyte cells and also in that sense,it has been infiltrated in the activation process of keratinocytes in the course of the plaque of psoriasis.Cell biological research on psoriasis has been established the suppression of epidermal T-cell density.Here we are interested to know how the cell biological system changes for introducing the half saturation constant in presence of suppression taking place DCs on the model dynamics.Our analytical and numerical result reveal that due to control effect,the macrophages population density does not impede for the interaction between T-cell and keratinocytes.T-cell and keratinocyte population ultimately become stable after a certain period of time span.