Toward ultrametric modeling of the epidemic spread

TL;DR

This paper introduces an ultrametric extension of the classical SIR epidemic model using hierarchical clustering and p-adic parameterization, providing new insights into epidemic spread management.

Contribution

It proposes a novel ultrametric SIR model based on hierarchical clustering and p-adic analysis, expanding the modeling framework for epidemics.

Findings

Ultrametric SIR model aligns with classical model in certain scenarios.

Hierarchical isolation strategies can effectively reduce epidemic spread.

Numerical analysis demonstrates the model's potential for epidemic management.

Abstract

An ultrametric model of epidemic spread of infections based on the classical SIR model is proposed. Ultrametrics on a set of individuals based on theire hierarchical clustering relativly to the average time of infectious contact is introduced. The general equations of the ultrametric SIR model are written down and their particular implementation using $p$-adic parameterization 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.