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 neighbours or to distant nodes via non-local diffusion, governed by a tunable probability parameter γ. To theoretically characterise 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 non-local traffic. By systematically analysing the effects of transmission capacity and diffusion strategies, we reveal that while the final epidemic size grows monotonically with non-local prevalence, the instantaneous infection peak exhibits a non-monotonic peak enhancement phenomenon. Specifically, an optimal mixture of local and non-local 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 optimising travel restrictions and preventing healthcare systems from being overwhelmed by unexpected infection surges, offering significant societal value.
Xiong et al. (Fri,) studied this question.