Extinction of Epidemics in Lattice Models with Quenched Disorder

TL;DR

This paper investigates how quenched disorder affects epidemic extinction in lattice models, revealing that disorder can enhance the contact process under certain conditions through analytical and numerical methods.

Contribution

It introduces a mapping of epidemic extinction in disordered lattices to an Anderson Hamiltonian, providing new insights into disorder's role in epidemic dynamics.

Findings

Disorder can enhance the contact process when mean parameters are unaffected.

Analytical mean-field analysis supports numerical results.

Numerical simulations confirm the disorder's impact on epidemic persistence.

Abstract

The extinction of the contact process in lattice models with quenched disorder is analysed in the limit of small density of infected sites. It is shown that the problem in such a regime can be mapped to the quantum-mechanical one characterized by the Anderson Hamiltonian for an electron in a random lattice. It is demonstrated both analytically (self-consistent mean-field) and numerically (by direct diagonalization of the Hamiltonian and by means of cellular automata simulations) that disorder enhances the contact process given the mean values of random parameters are not influenced by disorder.