# High Degree Vertices and Spread of Infections in Spatially Modelled Social Networks

## TL;DR

This paper investigates how high degree vertices influence infection spread in spatially modeled social networks, showing that less contagious high degree vertices tend to confine infections within communities, supported by theoretical analysis and simulations.

## Contribution

It introduces a spatial preferential attachment network model and analyzes the impact of high degree vertices' contagiousness on infection spread patterns.

## Key findings

- Infection tends to stay within communities when high degree vertices are less contagious.
- High degree vertices' contagiousness significantly affects whether infections jump between communities.
- Simulations support the theoretical results and conjectures.

## Abstract

We examine how the behaviour of high degree vertices in a network affects whether an infection spreads through communities or jumps between them. We study two stochastic susceptible-infected-recovered (SIR) processes and represent our network with a spatial preferential attachment (SPA) network. In one of the two epidemic scenarios we adjust the contagiousness of high degree vertices so that they are less contagious. We show that, for this scenario, the infection travels through communities rather than jumps between them. We conjecture that this is not the case in the other scenario, when contagion is independent of the degree of the originating vertex. Our theoretical results and conjecture are supported by simulations.