Mathematical Modeling of the Disease Psoriasis With Special Emphasis on Biologic Treatment

Psoriasis is a serious dermatological problem and worldwide 2-3 % of people (approx.) Are affected by this disease. Since its discovery in the early 19th century, many researchers Have struggled to find the exact roots of this disease and the useful treatment Strategy to control it. In 1979, researchers discovered the first clue that psoriasis is An autoimmune disease and in the latter part of the 20th century, the treatment of Psoriasis has undergone a revolution with the initiation of biological medications. This Thesis deals with some mathematical models to describe the etiology of psoriasis and The possible treatment strategies by introducing various biologics. In each chapter of This thesis, formulated models have been analyzed in two ways: theoretical analysis And numerical simulation. In the theoretical section, models have been formulated in such A way that their solutions are biologically reasonable. The existence, uniqueness, and Boundedness properties of these solutions enrich the plausibility of that models. The Effect of biologics has been demonstrated by considering the impulse differential equation And optimal control theory. Finally, numerical simulations have been performed to Illustrate each analytical finding.