Epidemic spreading driven by L-step random walks with stochastic resetting

To characterize the spatiotemporal impact of recurrent mobility, we propose a susceptible-infected-recovered model on complex networks driven by L-step random walks with stochastic resetting. By mapping microscopic mobility statistics onto an effective weighted directed network, we employ the dynamic message passing framework to characterize the macroscopic spreading dynamics and derive an interpretable mean-field threshold approximation. We identify the resetting probability γ as a pivotal control parameter: increasing γ modulates the effective topology from global connectivity to local confinement, inducing a continuous phase transition in outbreak size. Phase diagrams are used to quantify the competition between the mobility range L and resetting probability γ. Furthermore, we quantify exposure localization to explain the microscopic mechanism behind the observed transition. For highly infectious pathogens, the subcritical safety region undergoes a substantial reduction in size. These results show that mobility range and recurrent confinement form a quantifiable trade-off: for a fixed mobility length, increasing the resetting probability suppresses nonlocal exposure and reduces outbreak size, whereas larger mobility ranges or greater infectiousness require a higher critical resetting level to maintain the system below the epidemic threshold.