This paper is dedicated to the memory of Dietrich Stauffer, who was a pioneer in percolation theory and applications of it to problems of society, such as epidemiology. An epidemic is a percolation process gone out of control, that is, going beyond the critical transition threshold $p_c$. Here we discuss how the threshold is related to the basic infectivity of neighbors $R_0$, for trees (Bethe lattice), trees with triangular cliques, and in non-planar lattice percolation with extended-range connectivity. It is shown how having a smaller range of contacts increases the critical value of $R_0$ above the value $R_{0,c}=1$ appropriate for a tree, an infinite-range system or a large completely connected graph.

本文致力于纪念Dietrich Stauffer，他是渗流理论及其在社会问题（例如流行病学）中的应用的先驱。流行病是一个渗透过程失控，即超出了临界过渡阈值$p_C$。在这里，我们讨论阈值如何与邻居的基本传染性相关${\mathrm{[R}}_0$，适用于树木（Bethe晶格），具有三角形团的树木以及具有扩展范围连接性的非平面晶格渗滤。显示了较小的接触范围如何增加接触的临界值${\mathrm{[R}}_0$ 高于价值 ${\mathrm{[R}}_{0，C}=\mathrm{1个}$ 适用于树，无限范围系统或大型完全连接的图。