Clusters of infected individuals are defined on data from health laboratories, but this quantity has not been defined and characterized by epidemy models on statistical physics. For a system of mobile agents we simulate a model of infection without immunization and show that all the moments of...

We investigate the critical behavior of nonequilibrium phase transition from an active phase to an absorbing state on two selected fractal lattices, i.e., on a checkerboard fractal and on a Sierpinski carpet. The checkerboard fractal is finitely ramified with many dead ends, while the...

We analyze lattice–gas reaction–diffusion models which include spontaneous annihilation, autocatalytic creation, and diffusion of particles, and which incorporate the particle creation mechanisms of both Schloegl’s first and second models. For fixed particle diffusion or hop rate,...

For a two-dimensional system of agents modeled by molecular dynamics, we simulate epidemics spreading, which was recently studied on complex networks. Our resulting network model is time-evolving. We study the transitions to spreading as function of density, temperature and infection time. In...

We consider an epidemic model that extends the two-dimensional contact process by including more general processes of disease transmission and control. A hybrid approximation method that elaborates on the common pair approximation is proposed and shown to give very accurate predictions for the...

We review a recently devised Monte Carlo simulation method for the direct study of quasi-stationary properties of stochastic processes with an absorbing state. The method is used to determine the static correlation function and the interparticle gap-length distribution in the critical...

A model classically used for modelling the spread of an infectious diseases in a network is the time-continuous contact process, which is one simple example of an interacting particles system. It displays a non-equilibrium phase transition, related to the burst of an epidemic within a population...

A parametrization of generalised network clustering, in the form of four-motif prevalences, is presented. This involves three real parameters that are conditional on one-, two- and three-motif prevalences. Interpretations of these real parameters are presented that motivate a set of rewiring...