Effect of half-saturation in psoriatic pathogenesis using fractional derivative: A mathematical study

Abstract

Psoriasis is one type of prevalent chronic autoimmune inflammatory skin disorder characterized by T-Cells arbitrated hyperproliferation of epidermal Keratinocytes. Dendritic Cells have an important role to form this disease. On that outlook, we consider a mathematical model of Psoriasis consisting T-Cells, Dendritic Cells (DCs) and epidermal Keratinocytes through fractional-order differential equations along with impact of half-saturation constant. In this research article we observe, how T-Cells extremely stimulate a portion of Keratinocyte cells per day through their activation with
half maximal of the T-Cell density. We have established that the effect of half-saturation through exploring the suppressed memory, the inherited property of the system dynamics, in our mathematical model that contributes a greater impact for reducing the Keratinocyte cell population, causes the
disease Psoriasis.