Extinction of Epidemics in Lattice Models with Quenched Disorder

Details Extinction of Epidemics in Lattice Models with Quenched Disorder Extinction of Epidemics in Lattice Models with Quenched Disorder

2005-05-03

arxiv.org/abs/cond-mat/0505076v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

to appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.72.016111

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.

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