Stem Cell Based Fractional-Order Dynamical Model of Psoriasis: A Mathematical Study - Kushary, Subhankar; Ghosh, Tushar; Makinde, Oluwole Daniel; Li, Xue-Zhi; Roy, Priti Kumar (Department of Mathematics, Universitas Negeri Gorontalo, 2025)
Psoriasis is a chronic autoimmune skin disorder driven by dysregulated immune responses, where abnormal interactions between T cells and dendritic cells lead to excessive inflammatory cytokine production. This triggers the hyper-proliferation of epidermal keratinocytes while depleting mesenchymal stem cells (MSCs), which play a crucial role in immune modulation. The progression behavior of psoriasis is not only influenced by their present state but also by the historical evolution of underlying cellular interactions. Memory stages and complex interplay among immune components at different temporal scales significantly modulate disease expression. Motivated by this, we proposed a mathematical model of psoriasis to a fractional-order framework in order to incorporate memory-dependent effects and non-local characteristics. This article deals with a four-dimensional model of psoriasis involving concentrations of T cells, dendritic cells, keratinocytes, and mesenchymal stem cells (MSCs) in order to predict the temporal evolution in the considered cell densities during the disease dissemination process. Using Caputo, Caputo-Fabrizio, and Atangana-Baleanu-Caputo operators, we analyze how memory influences disease dynamics. In-depth mathematical analysis of the solution of the fractionalized model has been thoroughly investigated. The stability of the model is also examined using generalized Ulam–Hyers stability criteria. The considered population densities are numerically evaluated using various fractional orders with considered fractional operators to capture non-local effects. Optimal control is implemented on the fractionalized system using the Forward-Backward Sweep Method (FBSM), emphasizing the impacts of two biologics, namely TNF-α inhibitors and IL-23 blockers, via considered operators. Numerical simulations are performed in support of the theoretical analyses, accompanied by detailed discussions from both mathematical and biological viewpoints. Results based on optimal control effectiveness analysis indicate that a combined control strategy, particularly under the Caputo-Fabrizio operator, optimally reduces keratinocyte density. Which offers deeper insights into disease progression and effective therapeutic approaches.