Mathematical Models for Therapeutic Approaches to Control Psoriasis

Description

This book discusses several mathematical models highlighting the disease dynamics of psoriasis and its control. It explains the control of keratinocyte concentration through a negative feedback mechanism and the effect of including a realistic time delay in that system. The effect of cytokine release is described in a mathematical model of psoriasis and further elucidated in two different mathematical pathways: the ordinary differential equation model system, and the fractional-order differential equation model system. The book also identifies the role of CD8+ T-cells in psoriasis by investigating the interaction between dendritic cells and CD8+ T-cells. Presenting an approach to control the fractional-order system to prevent excess production of keratinocyte cell population, the book is intended for researchers and scientists in the field of applied mathematics, health informatics, applied statistics and qualitative public health, as well as bio-mathematicians interested in the mathematical modeling of autoimmune diseases like psoriasis. Front Matter ....Pages i-xvii Introduction (Priti Kumar Roy, Abhirup Datta)....Pages 1-4 Front Matter ....Pages 5-5 Basic Mathematical Model on Immunopathogenic Plaque of Psoriasis (Priti Kumar Roy, Abhirup Datta)....Pages 7-13 Release of Cytokine and Its Control During the Formation of Psoariasis (Priti Kumar Roy, Abhirup Datta)....Pages 15-23 Regulating Growth of Keratinocytes through Feedback Mechanism with Delay Effect in Psoriatic System (Priti Kumar Roy, Abhirup Datta)....Pages 25-35 Control of Psoriatic System for Logistic T-Cell Proliferation (Priti Kumar Roy, Abhirup Datta)....Pages 37-45 Incidental Effect of Half-Saturation on the Psoriatic Pathogenesis (Priti Kumar Roy, Abhirup Datta)....Pages 47-51 Inhibition of Excessive Keratinocyte Growth in Psoriasis using Drugs Cyclosporin and FK506 (Priti Kumar Roy, Abhirup Datta)....Pages 53-60 Front Matter ....Pages 61-62 Fractional Approach of the Formation of Psoriasis during Release of Cytokines (Priti Kumar Roy, Abhirup Datta)....Pages 63-68 Fractional Approach for Incidental Effect of Half-Saturation on the Psoriatic Pathogenesis (Priti Kumar Roy, Abhirup Datta)....Pages 69-74 Fractional Approach for the Inhibition of Excessive Keratinocyte Growth in Psoriasis using Drugs Cyclosporin and FK506 (Priti Kumar Roy, Abhirup Datta)....Pages 75-89