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A mathematical model of mitotic activity of epidermis in normal skin and skin afflicted with psoriasis is presented as a system of two autonomous nonlinear differential equations. Its qualitative analysis was carried out and numerical solutions were obtained at the parameter values corresponding to these states. It was shown that in the norm, a single stable equilibrium of a "focus" type exists in the system; whereas in psoriasis, owing to an increase in the growing fraction, hyperproliferation, and enhanced migration of interacting keratinocytes, a stable limit cycle arises from the state of unstable focus. In this paper we also report on the results of computer modeling of synchronization of self-excited oscillations of keratinocyte population density in psoriatic lesions by an external periodic force. This synchronization is viewed as a possible mechanism of the clinically observed dependence of psoriasis course on some natural factors of cyclic nature.

On the basis of the modern conceptions postulating that the growing layer of normal epidermis contains two populations of keratinocytes differing greatly in the rate of mitotic division (stem and transient cells), a hypothesis was proposed that explains the reason for the establishment of the portion of the proliferating fraction close to 60%. A relationship between this value and the distribution of keratinocytes of the basal layer in space was demonstrated, and formulae for its calculation were derived. Possible pathways of the transition from the normal spatial configuration to the distribution typical for the focal lesion in psoriasis were analyzed when all stem cells begin to divide vigorously, and the size of the population of transient cells is 100%.