We study the epidemic spreading on spatial networks where the probability that two nodes are connected decays with their distance as a power law. As the exponent of the distance dependence grows, model networks smoothly transition from the random network limit to the regular lattice limit. We show that despite keeping the average number of contacts constant, the increasing exponent hampers the epidemic spreading by making long-distance connections less frequent. The spreading dynamics is influenced by the distance-dependence exponent as well and changes from exponential growth to power-law growth. The observed power-law growth is compatible with recent analyses of empirical data on the spreading of COVID-19 in numerous countries.

我们研究了空间网络上的流行病传播，其中两个节点连接的概率以距离作为幂律而衰减。随着距离依赖指数的增长，模型网络从随机网络极限平稳过渡到规则晶格极限。我们表明，尽管保持平均接触数不变，但指数的增加却使远程连接的频率降低，从而阻碍了流行病的传播。扩散动力学也受距离依赖指数的影响，并且从指数增长到幂律增长也随之变化。观察到的幂律增长与最近对许多国家中COVID-19扩散的经验数据的分析相吻合。