Epidemic Synchronization and Mobility Susceptibility in Interconnected Urban Networks

Recent events, such as the COVID-19 pandemic, highlight how human mobility can turn local outbreaks into global crises. We study epidemic spread across interconnected cities using the SIR framework, where each city is a local population governed by differential equations. Coupling arises from a gravity-based mobility network, with flows increasing with population and decreasing with distance. Two parameters, mobility rate σ and return rate ρ, govern movement frequency. Simulations on Cayley networks show that low σ leads to asynchronous outbreaks in hubs, while high σ induces synchronized peaks across cities. A mobility susceptibility parameter quantifies how epidemic peaks respond to changes in σ, identifying critical regions where small mobility changes amplify spread. Our results show how mobility and network structure shape epidemic synchronization and can inform mitigation strategies.