A mathematical model of acne

The current study develops a mathematical model of acne. The model takes into account the characteristics of the appearance, maturation, and spread of pustules on the system of sweat glands of the skin. The process of bacterial population growth is described by a system of discrete-time equations. The treatment model assumes the direct effect of chemicals on the pustules. The statistical-probabilistic approach is applied in the model of the distribution of patients by the time of the onset of the stages of the condition and in the models of the distribution by the duration of treatment. The parameters that characterize the kinetics of pustule growth and the rate of their spread over the surface are determined based on clinical data. The treatment model assumes that the drugs affect all the pustules simultaneously.