Coupled effects of local movement and global interaction on contagion

TL;DR

This paper explores how local movement and global interactions jointly influence contagion spread, revealing that their coexistence broadens infection reach and that controlling movement and spatial segregation can mitigate epidemics.

Contribution

It introduces a coupled SIS model incorporating segregated spatial domains and individual linkages, analyzing their combined effects on contagion dynamics and epidemic thresholds.

Findings

Coexistence of local movement and global interaction widens disease spread.

Narrowing spatial domains and reducing mobility help control epidemics.

A log-log relation links infected individuals to the timescale τ.

Abstract

By incorporating segregated spatial domain and individual-based linkage into the SIS (susceptible-infected-susceptible) model, we investigate the coupled effects of random walk and intragroup interaction on contagion. Compared with the situation where only local movement or individual-based linkage exists, the coexistence of them leads to a wider spread of infectious disease. The roles of narrowing segregated spatial domain and reducing mobility in epidemic control are checked, these two measures are found to be conducive to curbing the spread of infectious disease. Considering heterogeneous time scales between local movement and global interaction, a log-log relation between the change in the number of infected individuals and the timescale $\tau$ is found. A theoretical analysis indicates that the evolutionary dynamics in the present model is related to the encounter probability and the encounter time. A functional relation between the epidemic threshold and the ratio of shortcuts, and a functional relation between the encounter time and the timescale $\tau$ are found.