Phase lag in epidemics on a network of cities

TL;DR

This paper analyzes how infection fluctuations synchronize across cities connected by commuting, revealing phase lags influenced by infection rate differences and coupling strength, supported by analytical and simulation results.

Contribution

It provides an analytical framework for understanding phase lag and synchronization in epidemic dynamics on city networks using the van Kampen expansion.

Findings

Oscillations are synchronized with a phase lag under certain conditions.

Analytic results agree with stochastic simulations.

Infection rate differences affect phase lag and synchronization.

Abstract

We study the synchronisation and phase-lag of fluctuations in the number of infected individuals in a network of cities between which individuals commute. The frequency and amplitude of these oscillations is known to be very well captured by the van Kampen system-size expansion, and we use this approximation to compute the complex coherence function that describes their correlation. We find that, if the infection rate differs from city to city and the coupling between them is not too strong, these oscillations are synchronised with a well defined phase lag between cities. The analytic description of the effect is shown to be in good agreement with the results of stochastic simulations for realistic population sizes.