Phase lag in epidemics on a network of cities

Area of Science:

• Epidemiology
• Network Science
• Mathematical Biology

Background:

• Understanding infectious disease spread in interconnected populations is crucial.
• Oscillations in infection numbers are common but their synchronization and phase relationships require detailed study.

Purpose of the Study:

• To investigate the synchronization and phase lag of infection fluctuations in a network of commuting cities.
• To develop an analytical model for predicting these synchronized dynamics.

Main Methods:

• Utilized the van Kampen system-size expansion to approximate oscillations.
• Computed the complex coherence function to quantify correlations between cities.
• Compared analytical results with stochastic simulations for validation.

Main Results:

• Identified synchronized oscillations in infection numbers between cities.
• Demonstrated a well-defined phase lag in these oscillations when infection rates vary and coupling is moderate.
• Analytical model showed good agreement with simulation results for realistic population sizes.

Conclusions:

• The van Kampen system-size expansion effectively describes synchronized disease dynamics in connected populations.
• Phase lags are a predictable feature of epidemic spread in networks with heterogeneous infection rates and moderate coupling.