Abstract
Psoriasis is a chronic skin disease in which the process of hyper-proliferation (excessive division) of skin cells starts. Externally, psoriasis appears as red papules, on the surface of which there are scales of white–gray color. There is substantial evidence that T-helper cells take vital accountability for creating the hyper-proliferation of keratinocytes (skin cells), which causes itching of skin patches. In this paper, we propose a mathematical model describing the concentrations of T-helper and keratinocyte cell populations to predict cellular behaviors for psoriasis regulation under normal or anomalous immune circumstances. Local and global asymptotic stabilities of the model equilibria are investigated. Additionally, by introducing two scalar bounded controls into the model, the effect of combined immunotherapy using IL-10 and IL-22 inhibitors is analyzed. The optimal control problem of minimizing the cost of immune therapy and simultaneous optimizing the effect of this therapy on T-helper cells and keratinocytes proliferation is formulated and solved by applying the Pontryagin maximum principle. Within the restrictions of the proposed model, the obtained analytical and numerical outcomes suggest that the optimal strategy of injecting IL-10 and IL-22 inhibitors can be effective for psoriasis treatment.
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