Abstract <p>A mathematical model for treating psoriasis is considered. The model consists of three differential equations that describe the relations between the major cell populations that are responsible for the occurrence, progression, and treatment of this disease. The model also contains a bound control function reflecting the effects of a drug aimed at inhibiting interactions between specific cell populations. The task is to reduce the population of cells directly affecting the disease at the end of a given period of time. The optimal control problem is analyzed using the Pontryagin maximum principle. The focus is on clarifying the bang-bang property of the corresponding optimal control, along with the possibility of singular regimens of different orders, depending on the relationships between the parameters of the original model.</p>