The spread of an infectious disease is well approximated by metapopulation networks connected by human mobility flow and upon which an epidemiological model is defined. In order to account for travel restrictions or cancellation we introduce a model with a parameter that explicitly indicates the ratio between the time scales of the intervening processes. We study the critical properties of the epidemic process and its dependence on such a parameter. We find that the critical threshold separating the absorbing state from the active state depends on the scale parameter and exhibits a critical behavior itself: a metacritical point – a critical value in the curve of critical points – reflected in the behavior of the attack rate measured for a wide range of empirical metapopulation systems. Our results have potential policy implications, since they establish a non-trivial critical behavior between temporal scales of reaction (epidemic spread) and diffusion (human mobility) processes.

传染病的传播可以通过由人类流动流动连接的元种群网络很好地近似，并在此基础上定义了流行病学模型。为了说明旅行限制或取消，我们引入了一个带有参数的模型，该参数明确指示干预过程的时间尺度之间的比率。我们研究流行过程的关键特性及其对此类参数的依赖。我们发现，将吸收状态与活动状态分开的临界阈值取决于尺度参数，并表现出临界行为本身：一个元临界点——临界点曲线中的临界值——反映在测量的攻击率的行为中范围广泛的经验性元种群系统。我们的结果具有潜在的政策含义，