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Related papers: Critical scaling of stochastic epidemic models

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The spreading of epidemics is very much determined by the structure of the contact network, which may be impacted by the mobility dynamics of the individuals themselves. In confined scenarios where a small, closed population spends most of…

Physics and Society · Physics 2018-05-09 Clara Granell , Peter J. Mucha

A stochastic epidemic model accounting for the effect of contact-tracing on the spread of an infectious disease is studied. Precisely, individuals identified as infected may contribute to detecting other infectious individuals by providing…

Probability · Mathematics 2009-03-28 Stéphan Clémençon , Viet Chi Tran , Hector De Arazoza

We study the Susceptible-Infectious-Susceptible (SIS) model on arbitrary networks. The well-established pair approximation treats neighboring pairs of nodes exactly while making a mean field approximation for the rest of the network. We…

Social and Information Networks · Computer Science 2026-05-05 George Cantwell , Cristopher Moore

We propose an extension of the classical susceptible infectious recovered (SIR) model that incorporates the effects of spatial propagation of an epidemic through a small number of additional compartments. The model is designed to capture…

Numerical Analysis · Mathematics 2026-03-02 M. Soledad Aronna , Mariana Bergonzi , Ernesto Kofman

In this paper we study the diffusion of an SIS-type epidemics on a network under the presence of a random environment, that enters in the definition of the infection rates of the nodes. Accordingly, we model the infection rates in the form…

Probability · Mathematics 2016-07-25 Stefano Bonaccorsi , Stefania Ottaviano

Throughout the course of an epidemic, the rate at which disease spreads varies with behavioral changes, the emergence of new disease variants, and the introduction of mitigation policies. Estimating such changes in transmission rates can…

Methodology · Statistics 2022-11-29 Jenny Huang , Raphaël Morsomme , David Dunson , Jason Xu

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 $N\to\infty$.…

Probability · Mathematics 2021-12-01 Xinghua Zheng , Qingsan Zhu

We consider the SIR model and study the first time the number of infected individuals begins to decrease and the first time this population is below a given threshold. We interpret these times as functions of the initial susceptible and…

Classical Analysis and ODEs · Mathematics 2020-09-23 Ryan Hynd , Dennis Ikpe , Terrance Pendleton

We study the qualitative properties of a spatial diffusive heterogeneous SIR model, that appears in mathematical epidemiology to describe the spread of an infectious disease in a population. The model we consider consists in a system of…

Analysis of PDEs · Mathematics 2020-05-15 Romain Ducasse

The stochastic SIRS model is a continuous-time Markov chain modelling the spread of infectious diseases with temporary immunity, in a homogeneously-mixing population of fixed size $N$. We study the scaling behaviour of the extinction time…

Probability · Mathematics 2021-01-14 Jingran Zhai

The critical behavior of the stochastic susceptible-infected-recovered model on a square lattice is obtained by numerical simulations and finite-size scaling. The order parameter as well as the distribution in the number of recovered…

Disordered Systems and Neural Networks · Physics 2011-03-07 David R. de Souza , Tânia Tomé , Robert M. Ziff

Modeling long-range epidemic spreading in a random environment, we consider a quenched disordered, $d$-dimensional contact process with infection rates decaying with the distance as $1/r^{d+\sigma}$. We study the dynamical behavior of the…

Disordered Systems and Neural Networks · Physics 2015-04-02 R. Juhász , I. A. Kovács , F. Iglói

In this paper, a susceptible-infected-susceptible (SIS) model with identical infectivity, where each node is assigned with the same capability of active contacts, $A$, at each time step, is presented. We found that on scale-free networks,…

Physics and Society · Physics 2007-05-23 Rui Yang , Jie Ren , Wen-Jie Bai , Tao Zhou , Ming-Feng Zhang , Bing-Hong Wang

In a collection of particles performing independent random walks on $\mathbb Z^d$ we study the spread of an infection with SIR dynamics. Susceptible particles become infected when they meet an infected particle. Infected particles heal and…

Probability · Mathematics 2022-09-14 Duncan Dauvergne , Allan Sly

The pattern formation and spatial spread of infectious populations are investigated using a kernel-based Susceptible-Infectious-Recovered (SIR) model applicable across a wide range of basic reproduction numbers $R_o$. The focus is on the…

Physics and Society · Physics 2022-09-13 Shuolin Li , Craig Henriquez , Gabriel Katul

We consider a spatial SIR epidemic model where the infectivity of infected individuals depends upon their age of infection, and infections are non local. The domain is an unbounded subset of $\R^d$,and the individuals do not move. We extend…

Probability · Mathematics 2025-11-18 Armand Kanga , Etienne Pardoux

We study a multilayer SIR model with two levels of mixing, namely a global level which is uniformly mixing, and a local level with two layers distinguishing household and workplace contacts, respectively. We establish the large population…

Probability · Mathematics 2023-10-27 Madeleine Kubasch

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…

Probability · Mathematics 2018-02-23 Graham Brightwell , Thomas House , Malwina Luczak

I present three models of plant--pathogen interactions. The models are stochastic and spatially explicit at the scale of individual plants. For each model, I use a version of pair approximation or moment closure along with a separation of…

Numerical Analysis · Mathematics 2025-10-20 David H. Brown

We study the phase transition from the persistence phase to the extinction phase for the SIRS (susceptible/ infected/ refractory/ susceptible) model of diseases spreading on the networks. We derive an analytical expression of the…

Populations and Evolution · Quantitative Biology 2019-11-18 M. Ali Saif