Impacts of preference and geography on epidemic spreading

TL;DR

This paper explores how preference and geography influence epidemic spreading on a growing network, revealing conditions under which diseases persist or die out based on network parameters.

Contribution

It introduces a model combining preferential attachment and geographical distance effects, analyzing their impact on epidemic thresholds and network robustness.

Findings

Network becomes more robust with higher preference parameter A.

Geographical constraints (B) affect epidemic thresholds.

Critical behavior depends on the balance between A and B.

Abstract

We investigate the standard susceptible-infected-susceptible model on a random network to study the effects of preference and geography on diseases spreading. The network grows by introducing one random node with $m$ links on a Euclidean space at unit time. The probability of a new node $i$ linking to a node $j$ with degree $k_j$ at distance $d_{ij}$ from node $i$ is proportional to $k_{j}^{A}/d_{ij}^{B}$, where $A$ and $B$ are positive constants governing preferential attachment and the cost of the node-node distance. In the case of A=0, we recover the usual epidemic behavior with a critical threshold below which diseases eventually die out. Whereas for B=0, the critical behavior is absent only in the condition A=1. While both ingredients are proposed simultaneously, the network becomes robust to infection for larger $A$ and smaller $B$.