Modeling and control of psoriasis

In this paper a mathematical model of psoriasis is created and investigated. The model is described by a nonlinear control system of three differential equations involving the concentration of Dendritic Cells (Tissues Macrophages), T-Lymphocytes and Keratinocytes. Analytical and numerical studies techniques will be discussed. An optimal control problem of minimizing the release of Keratinocytes to standardize the growth of the Dendritic Cells is stated and solved using Pontryagin Maximum Principle. Optimal solution and optimal controls are presented at different values of the model.