Epidemic spreading driven by local and nonlocal random walks on complex networks

In this paper, we investigate the dynamics of epidemics spreading driven via a hybrid random walk mechanism on complex networks. In this framework, transmission is mediated by infection packets that propagate either to local neighbors or to distant nodes via nonlocal diffusion, governed by a tunable probability parameter [Formula: see text]. To theoretically characterize this stochastic process, we derive a Dynamic Message Passing (DMP) formulation. This analytical framework provides a description of the system dynamics, and accurately solves the complex correlations arising from the interplay between local topology and nonlocal traffic. By systematically analyzing the effects of transmission capacity and diffusion strategies, we reveal that while the final epidemic size grows monotonically with nonlocal prevalence, the instantaneous infection peak exhibits a nonmonotonic peak enhancement phenomenon. Specifically, an optimal mixture of local and nonlocal spreading generates a more intense outbreak peak than either pure strategy alone, revealing a synergistic mechanism between local saturation and global exploration. These findings highlight hidden risks in hybrid mobility patterns, and provide theoretical guidance to policymakers on optimizing travel restrictions and preventing healthcare systems from being overwhelmed by unexpected infection surges, offering significant societal value.