Reaction–diffusion processes¹ have been widely used to study dynamical processes in epidemics^2,3,4 and ecology⁵ in networked metapopulations. In the context of epidemics⁶, reaction processes are understood as contagions within each subpopulation (patch), while diffusion represents the mobility of individuals between patches. Recently, the characteristics of human mobility⁷, such as its recurrent nature, have been proven crucial to understand the phase transition to endemic epidemic states^8,9. Here, by developing a framework able to cope with the elementary epidemic processes, the spatial distribution of populations and the commuting mobility patterns, we discover three different critical regimes of the epidemic incidence as a function of these parameters. Interestingly, we reveal a regime of the reaction–diffussion process in which, counter-intuitively, mobility is detrimental to the spread of disease. We analytically determine the precise conditions for the emergence of any of the three possible critical regimes in real and synthetic networks.

反应扩散过程¹已被广泛用于研究网络化种群中流行病^2、3、4和生态学^5的动力学过程。在流行病⁶的背景下，反应过程应理解为每个亚群（斑块）内的传染，而扩散则代表个体在斑块之间的流动性。最近，人们已经证明了人类流动性⁷的特征（例如其复发性）对于理解向流行病的相变至关重要^8,9。。在这里，通过开发一个能够应对基本的流行过程，人口的空间分布和通勤交通方式的框架，我们发现了流行病发病率的三个不同的关键机制，这些机制是这些参数的函数。有趣的是，我们揭示了一种反应-扩散过程的机制，在这种情况下，与直觉相反，流动性不利于疾病的传播。我们通过分析确定了在实际网络和综合网络中出现三种可能的关键机制中的任何一种的精确条件。