Spreading properties for SIR models on homogeneous trees

TL;DR

This paper analyzes how the spread of an SIR epidemic model varies on homogeneous trees, revealing new spreading behaviors and critical interaction thresholds depending on the tree's degree.

Contribution

It introduces a detailed study of SIR epidemic spreading on homogeneous trees, highlighting the impact of tree degree and interaction strength on epidemic propagation.

Findings

Spreading properties resemble the lattice case when degree is one.

New spreading features emerge for degrees larger than two.

A critical interaction strength exists beyond which epidemic spreading stops.

Abstract

We consider an epidemic model of SIR type set on a homogeneous tree and investigate the spreading properties of the epidemic as a function of the degree of the tree, the intrinsic basic reproduction number and the strength of the interactions within the population of infected individuals. When the degree is one, the homogeneous tree is nothing but the standard lattice on the integers and our model reduces to a SIR model with discrete diffusion for which the spreading properties are very similar to the continuous case. On the other hand, when the degree is larger than two, we observe some new features in the spreading properties. Most notably, there exists a critical value of the strength of interactions above which spreading of the epidemic in the tree is no longer possible.