Related papers: Two-dimensional SIR epidemics with long range infe…
We study supercritical spatial SIR epidemics on $\mathbb{Z}^2\times \{1,2,\ldots, N\}$, where each site in $\mathbb{Z}^2$ represents a village and $N$ stands for the village size. We establish several key asymptotic results as $N\to\infty$.…
This paper is devoted to the study of a stochastic epidemiological model which is a variant of the SIR model to which we add an extra factor in the transition rate from susceptible to infected accounting for the inflow of infection due to…
In this work, we study the evolution of the susceptible individuals during the spread of an epidemic modeled by the susceptible-infected-recovered (SIR) process spreading on the top of complex networks. Using an edge-based compartmental…
This article is devoted to the analysis of a particle system model for epidemics among a finite population with susceptible, infective and removed individuals (SIR). The infection mechanism depends on the relative distance between…
We present a stochastic model for two successive SIR (Susceptible, Infectious, Recovered) epidemics in the same network structured population. Individuals infected during the first epidemic might have (partial) immunity for the second one.…
We investigate the time-evolution and steady states of the stochastic susceptible-infected-recovered-susceptible(SIRS) epidemic model on one- and two- dimensional lattices. We compare the behavior of this system, obtained from computer…
We study the absorbing phase transition for the model of epidemic spreading, Susceptible- Infected- Refractory (SIR), on one dimensional small world networks. This model has been found to be in the universality class of the dynamical…
We considered the Asynchronous SIR (susceptible-infected-removed) model on Penrose and Ammann-Beenker quasiperiodic lattices, and obtained its critical behavior by using Newman-Ziff algorithm to track cluster propagation by making a tree…
A stochastic SIR (susceptible $\to$ infective $\to$ recovered) epidemic model defined on a social network is analysed. The underlying social network is described by an Erd\H{o}s-R\'{e}nyi random graph but, during the course of the epidemic,…
The effect of spatial correlations on the spread of infectious diseases was investigated using a stochastic SIR (Susceptible-Infective-Recovered) model on complex networks. It was found that in addition to the reduction of the effective…
In this paper, we study the dynamics of the susceptible-infected-recovered (SIR) model on a network with community structure, namely the stochastic block model (SBM). As usual, the SIR model is a stochastic model for an epidemic where…
In this paper we are concerned with the two-stage contact process on the lattice $\mathbb{Z}^d$ introduced in \cite{Krone1999}. We gives a limit theorem of the critical infection rate of the process as the dimension $d$ of the lattice grows…
An epidemic model with births and deaths is considered on a two dimensional LxL lattice. Each individual can have global infective contacts according to the standard SIR model rules or local infective contacts with its nearest neighbors. We…
Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights…
We perform large-scale simulations of the two-dimensional long-range bond percolation model with algebraically decaying percolation probabilities $\sim 1/r^{2+\sigma}$, using both conventional ensemble and event-based ensemble methods for…
In this paper, we propose a modified susceptible-infected-recovered (SIR) model, in which each node is assigned with an identical capability of active contacts, $A$, at each time step. In contrast to the previous studies, we find that on…
We use the connection between bond percolation and SIR epidemics to establish lower bounds for the critical percolation probability in $2$ and $3$ dimensions as the range becomes large. The bound agrees with the conjectured asymptotics for…
The supercritical series expansion of the survival probability for the one-dimensional contact process in heterogeneous and disordered lattices is used for the evaluation of the loci of critical points and critical exponents $\beta$. The…
Epidemic propagation on complex networks has been widely investigated, mostly with invariant parameters. However, the process of epidemic propagation is not always constant. Epidemics can be affected by various perturbations, and may bounce…
We exhibit a scaling law for the critical SIS stochastic epidemic: If at time 0 the population consists of square root N infected and N - square root N susceptible individuals, then when time and number currently infected are both scaled by…