Abstract: An ultrametric model of epidemic spread of infections based on the classical SIR model is proposed. Ultrametrics on a set of individuals is introduced based on their hierarchical clustering relative to the average time of infection contact. The general equations of the ultrametric SIR model are written down and their particular implementation using the p-adic parametrization is presented. A numerical analysis of the p-adic SIR model and a comparison of its behavior with the classical SIR model are performed. The concept of hierarchical isolation and the scenario of its management in order to reduce the level of epidemic spread is considered. © 2020, Pleiades Publishing, Ltd.