| Summary: | We present a mathematical model of disease (say a virus) spread that takes into account the hierarchic structure of social clusters in a population. It describes the dependence of epidemic’s dynamics on the strength of barriers between clusters. These barriers are established by authorities as preventative measures; partially they are based on existing socio-economic conditions. We applied the theory of random walk on the energy landscapes represented by ultrametric spaces (having tree-like geometry). This is a part of statistical physics with applications to spin glasses and protein dynamics. To move from one social cluster (valley) to another, a virus (its carrier) should cross a social barrier between them. The magnitude of a barrier depends on the number of social hierarchy levels composing this barrier. Infection spreads rather easily inside a social cluster (say a working collective), but jumps to other clusters are constrained by social barriers. The model implies the power law, <inline-formula><math display="inline"><semantics><mrow><mn>1</mn><mo>−</mo><msup><mi>t</mi><mrow><mo>−</mo><mi>a</mi></mrow></msup><mo>,</mo></mrow></semantics></math></inline-formula> for approaching herd immunity, where the parameter <i>a</i> is proportional to inverse of one-step barrier <inline-formula><math display="inline"><semantics><mrow><mo>Δ</mo><mo>.</mo></mrow></semantics></math></inline-formula> We consider linearly increasing barriers (with respect to hierarchy), i.e., the <i>m</i>-step barrier <inline-formula><math display="inline"><semantics><mrow><msub><mo>Δ</mo><mi>m</mi></msub><mo>=</mo><mi>m</mi><mo>Δ</mo><mo>.</mo></mrow></semantics></math></inline-formula> We also introduce a quantity characterizing the process of infection distribution from one level of social hierarchy to the nearest lower levels, spreading entropy <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">E</mi><mo>.</mo></mrow></semantics></math></inline-formula> The parameter <i>a</i> is proportional to <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">E</mi><mo>.</mo></mrow></semantics></math></inline-formula>
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