Utrametric diffusion model for spread of covid-19 in socially clustered population: Can herd immunity be approached in Sweden?

We present a new mathematical model of disease spread reflecting specialties of covid-19 epidemic by elevating the role social clustering of population. The model can be used to explain slower approaching herd immunity in Sweden, than it was predicted by a variety of other mathematical models; see graphs Fig. 2. The hierarchic structure of social clusters is mathematically modeled with ultrametric spaces having treelike geometry. To simplify mathematics, we consider homogeneous trees with p -branches leaving each vertex. Such trees are endowed with algebraic structure, the p -adic number fields. We apply theory of the p -adic diffusion equation to describe coronavirus’ 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, the 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. As the most appropriate for the recent situation in Sweden, we consider linearly increasing barriers . This structure matches with mild regulations in Sweden. The 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. We present socio-medical specialties of the covid-19 epidemic supporting our purely diffusional model.