Virus spread and voter model on random graphs with multiple type nodes

TL;DR

This paper investigates how multiple node types affect epidemic and opinion spread on various random graphs, comparing vaccination strategies and opinion dissemination effectiveness.

Contribution

It introduces an analysis of multi-type node effects on epidemic and opinion dynamics across different random graph models.

Findings

Vaccination strategies vary in effectiveness depending on node types.

Optimal opinion dissemination depends on initial node placement.

Multiple node types significantly influence spread dynamics.

Abstract

When modelling epidemics or spread of information on online social networks, it is crucial to include not just the density of the connections through which infections can be transmitted, but also the variability of susceptibility. Different people have different chance to be infected by a disease (due to age or general health conditions), or, in case of opinions, ones are easier to be convinced by others, or stronger at sharing their opinions. The goal of this work is to examine the effect of multiple types of nodes on various random graphs such as Erd\H{o}s--R\'enyi random graphs, preferential attachment random graphs and geometric random graphs. We used two models for the dynamics: SEIR model with vaccination and a version of voter model for exchanging opinions. In the first case, among others, various vaccination strategies are compared to each other, while in the second case we studied sevaral initial configurations to find the key positions where the most effective nodes should be placed to disseminate opinions.