We present a new mathematical model of disease spread reflecting some specialties of the COVID-19 epidemic by elevating the role of hierarchic social clustering of population. The model can be used to explain slower approaching herd immunity, e.g., in Sweden, than it was predicted by a variety of other mathematical models and was expected by epidemiologists; see graphs Fig. 1, 2. The hierarchic structure of social clusters is mathematically modeled with ultrametric spaces having treelike geometry. To simplify mathematics, we consider trees with the constant number $p>1$ of branches leaving each vertex. Such trees are endowed with an algebraic structure, these are $p$-adic number fields. We apply theory of the $p$-adic diffusion equation to describe a virus spread in hierarchically clustered population. This equation has applications to statistical physics and microbiology for modeling dynamics on energy landscapes. 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’s levels composing this barrier. We consider linearly increasing barriers. A virus spreads rather easily inside a social cluster (say working collective), but jumps to other clusters are constrained by social barriers. This behavior matches with the COVID-19 epidemic, with its cluster spreading structure. Our model differs crucially from the standard mathematical models of spread of disease, such as the SIR-model; in particular, by notion of the probability to be infected (at time $t$ in a social cluster $C$). We present socio-medical specialties of the COVID-19 epidemic supporting our model.

我们 $p$ 雷森 $t$ 疾病的新数学模型 $p$ 阅读反映一些专业的内容 $C$ OVID-19 通过提升人口等级社会集群的作用而流行。该模型可用于解释群体免疫的实现速度较慢，例如在瑞典，其速度比各种其他数学模型的预测和流行病学家的预期要慢；见图 1、2。社会集群的层次结构是用具有树状几何形状的超度量空间进行数学建模的。为了简化数学，我们考虑具有常数的树$\mathrm{<span\; data-immersive-translate-walked="5cfcc357-e3b3-48e2-a192-7ffe99c03f93">p</span>}<span\; data-immersive-translate-walked="5cfcc357-e3b3-48e2-a192-7ffe99c03f93">></span>\mathrm{<span\; data-immersive-translate-walked="5cfcc357-e3b3-48e2-a192-7ffe99c03f93">1</span>}$离开每个顶点的分支。这些树被赋予了代数结构，它们是$\mathrm{<span\; data-immersive-translate-walked="5cfcc357-e3b3-48e2-a192-7ffe99c03f93">p</span>}$ -adic 数字字段。我们应用理论$\mathrm{<span\; data-immersive-translate-walked="5cfcc357-e3b3-48e2-a192-7ffe99c03f93">p</span>}$ -adic扩散方程描述病毒在分层聚集群体中的传播。该方程可应用于统计物理学和微生物学，用于对能源景观的动力学进行建模。为了从一个社会集群（山谷）转移到另一个社会集群（山谷），病毒（其携带者）应该跨越它们之间的社会障碍。障碍的大小取决于构成该障碍的社会等级的数量。我们考虑线性增加的障碍。病毒在一个社会群体（比如工作集体）内相当容易传播，但跳跃到其他群体则受到社会障碍的限制。这种行为与 COVID-19 疫情的集群传播结构相匹配。 我们的模型与疾病传播的标准数学模型（例如 SIR 模型）有很大不同；特别是，通过感染概率的概念（在时间$\mathrm{<span\; data-immersive-translate-walked="5cfcc357-e3b3-48e2-a192-7ffe99c03f93">t</span>}$在一个社会群体中$\mathrm{<span\; data-immersive-translate-walked="5cfcc357-e3b3-48e2-a192-7ffe99c03f93">C</span>}$ ）。我们介绍了支持我们模型的 COVID-19 流行病的社会医学专业。