Spatiotemporal contagion dynamics driven by human mobility in multilayer activity-driven networks

Expanding transport systems have disrupted the geographical boundaries of human mobility, producing intricate patterns of spatiotemporal contagion dynamics. Conventional theoretical models often neglect the memory effect of human mobility and the dynamic evolution of social interactions. To address this problem, we introduce a novel theoretical framework for modeling spatiotemporal contagion dynamics. We first develop a temporal multilayer network that integrates the spatial structure of populations with a non-instantaneous travel process, where infections occur both within layers and during transit, facilitated by time-varying social interactions modeled via activity-driven networks. Second, we formulate the non-Markovian dynamics using quenched mean-field theory and derive an analytical epidemic threshold based on the Next Generation Matrix approach, demonstrating that the onset and progression of epidemics are governed by travel strength (proportion of travelers and hopping rate), interaction density, and travel duration. Third, through extensive experiments and analysis, we find that, compared to Markovian dynamics and analytical SIR-type solutions, non-Markovian dynamics introduce memory-driven delays in the redistribution of effective population size across structural components, capturing realistic multi-wave infection patterns more accurately. Dense travel interactions predominantly drive spatiotemporal contagion dynamics. In highly connected travel environments, stronger travel strength consistently accelerates epidemic spread. In contrast, the impact of travel duration is more complex and depends on transmission rate, reflecting the interplay of infection and recovery during transit. This study offers critical theoretical insights for designing public health interventions, such as travel restrictions and quarantine measures, to mitigate pandemic risks.