Percolation and the pandemic

Abstract

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.

For special edition of Physica A in memory of Dietrich Stauffer

References in corpus (10)

• Continuum Percolation Thresholds in Two Dimensions
• On the critical behavior of the Susceptible-Infected-Recovered (SIR) model on a square lattice
• Exact bond percolation thresholds in two dimensions
• Site percolation on square and simple cubic lattices with extended neighborhoods and their continuum limit
• Simple cubic random-site percolation thresholds for neighborhoods containing fourth-nearest neighbors
• Universal condition for critical percolation thresholds of kagome-like lattices
• Critical polynomials in the nonplanar and continuum percolation models
• Bond percolation thresholds on Archimedean lattices from critical polynomial roots
• Percolation in the canonical ensemble
• Percolation thresholds for discorectangles: numerical estimation for a range of aspect ratios

Cited by in corpus (25)

• Site percolation on square and simple cubic lattices with extended neighborhoods and their continuum limit
• Universal behavior of site and bond percolation thresholds on regular lattices with compact extended-range neighborhoods in 2 and 3 dimensions
• Percolation thresholds on triangular lattice for neighbourhoods containing sites up-to the fifth coordination zone
• Periodic recurrent waves of Covid-19 epidemics and vaccination campaign
• Metastable states in plateaus and multi-wave epidemic dynamics of Covid-19 spreading in Italy
• Site and bond percolation on four-dimensional simple hypercubic lattices with extended neighborhoods
• Spreading processes in "post-epidemic" environments
• Exact percolation probabilities for a square lattice: Site percolation on a plane, cylinder, and torus
• Effectiveness of Contact Tracing on Networks with Cliques
• Random site percolation thresholds on square lattice for complex neighborhoods containing sites up to the sixth coordination zone
• Site percolation in distorted square and simple cubic lattices with flexible number of neighbors
• Continuum Percolation and Stochastic Epidemic Models on Poisson and Ginibre Point Processes
• Universality of random-site percolation thresholds for two-dimensional complex non-compact neighborhoods
• A robust prediction from a minimal model of COVID-19 -- Can we avoid the third wave?
• Characterizing spatial point processes by percolation transitions
• A branching random-walk model of disease outbreaks and the percolation backbone
• Epidemic spreading in an expanded parameter space: the supercritical scaling laws and subcritical metastable phases
• Universality of percolation at dynamic pseudocritical point
• Bond percolation in distorted square and triangular lattices
• Modelling the Spread of an Epidemic in Presence of Vaccination using Cellular Automata
• Critical points of the random cluster model with Newman-Ziff sampling
• Site and bond percolation in linearly distorted triangular and square lattices
• Does social distancing matter for infectious disease propagation? A SEIR model and Gompertz law based cellular automaton
• Extended-range percolation in five dimensions
• Critical and quasicritical behavior in a three-species dynamical model of semi-directed percolation