Extinction of Epidemics in Lattice Models with Quenched Disorder

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.