Epidemic dynamics on metapopulation networks with node2vec mobility

TL;DR

This paper investigates how complex mobility rules, specifically node2vec, influence epidemic thresholds in metapopulation networks, revealing that certain mobility patterns can suppress or facilitate epidemic spread.

Contribution

It introduces a novel mapping of node2vec mobility to a first-order random walk and analyzes its impact on epidemic thresholds in metapopulation models.

Findings

Epidemic threshold increases when individuals rarely backtrack or visit common neighbors.

Node2vec mobility effects are comparable to changes in diffusion rates.

Mobility patterns significantly influence epidemic spreading dynamics.

Abstract

Metapopulation models have been a powerful tool for both theorizing and simulating epidemic dynamics. In a metapopulation model, one considers a network composed of subpopulations and their pairwise connections, and individuals are assumed to migrate from one subpopulation to another obeying a given mobility rule. While how different mobility rules affect epidemic dynamics in metapopulation models has been studied, there have been relatively few efforts on comparison of the effects of simple (i.e., unbiased) random walks and more complex mobility rules. Here we study a susceptible-infectious-susceptible (SIS) dynamics in a metapopulation model, in which individuals obey a parametric second-order random-walk mobility rule called the node2vec. We map the second-order mobility rule of the node2vec to a first-order random walk in a network whose each node is a directed edge connecting a pair of subpopulations and then derive the epidemic threshold. For various networks, we find that the epidemic threshold is large (therefore, epidemic spreading tends to be suppressed) when the individuals infrequently backtrack or infrequently visit the common neighbors of the currently visited and the last visited subpopulations than when the individuals obey the simple random walk. The amount of change in the epidemic threshold induced by the node2vec mobility is in general not as large as, but is sometimes comparable with, the one induced by the change in the diffusion rate for individuals.