Percolation and the pandemic

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