Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Covid-19: Why Herd Immunity was not Approached Anywhere? Ultrametric Diffusion Modeling of Virus Spread in Hierarchically Clustered Population

Version 1 : Received: 6 June 2021 / Approved: 7 June 2021 / Online: 7 June 2021 (09:16:21 CEST)

How to cite: Khrennikov, A. Covid-19: Why Herd Immunity was not Approached Anywhere? Ultrametric Diffusion Modeling of Virus Spread in Hierarchically Clustered Population. Preprints 2021, 2021060155 (doi: 10.20944/preprints202106.0155.v1). Khrennikov, A. Covid-19: Why Herd Immunity was not Approached Anywhere? Ultrametric Diffusion Modeling of Virus Spread in Hierarchically Clustered Population. Preprints 2021, 2021060155 (doi: 10.20944/preprints202106.0155.v1).

Abstract

In spite of numerous predictions, the natural herd immunity for covid-19 visru had not been approahed anywhere in the world. Thus, the traditional mathematical models of disease spread demonstrated their inability to describe adequately the covid-19 pandemic. In author's works, the novel model of the disease spread was developed. This model reflects the basic features of the covid-19 pandemic: a) the social clustering character of virus spread, b) . Social clustering is mathematically modelled with ultrametric spaces having the treelike geometry encoding hierarchy of the regulation constraints. The virus spread is described by ultrametric diffusion or random walk on the hierarchic energy landscape. In contrast to the standard models which are characterized by the exponential decrease of the probability to become infected - at the stage of approaching of the herd immunity, the ultrametric model is characterized by the power law. Moreover, the model gives the possibility to quantify the influence of restriction measures up to the lockdown. Our main result is that the play with restrictions, including lockdowns, is counterproductive and leads to the essential slowdown of approaching the herd immunity or even makes this impossible.

Keywords

disease spread; herd immunity; hierarchy of social clusters; ultrametric spaces; trees; social barriers; linear growing barriers; energy landscapes

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