Spatial Disease Propagation With Hubs

TL;DR

This paper models disease spread through spatial agents and hubs using a bipartite geometric graph, highlighting how the range of agent-hub connections influences epidemic percolation thresholds.

Contribution

It introduces a spatial point process model for disease transmission via hubs and analyzes how connection range affects percolation in the network.

Findings

Percolation threshold depends on the support of the connection function.

Long-distance travel significantly impacts disease spread.

Critical hub density is dictated by connection function support.

Abstract

Physical contact or proximity is often a necessary condition for the spread of infectious diseases. Common destinations, typically referred to as hubs or points of interest, are arguably the most effective spots for the type of disease spread via airborne transmission. In this work, we model the locations of individuals (agents) and common destinations (hubs) by random spatial point processes in $\mathbb{R}^d$ and focus on disease propagation through agents visiting common hubs. The probability of an agent visiting a hub depends on their distance through a connection function $f$. The system is represented by a random bipartite geometric (RBG) graph. We study the degrees and percolation of the RBG graph for general connection functions. We show that the critical density of hubs for percolation is dictated by the support of the connection function $f$, which reveals the critical role of long-distance travel (or its restrictions) in disease spreading.