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In this paper, we are concerned with stochastic susceptible-exposed-infected-removed epidemics on complete graphs with vertex-dependent transition rates. Large and moderate deviations of empirical density fields of our models are given.…

Probability · Mathematics 2023-05-02 Xiaofeng Xue , Xueting Yin

Compartmental models like the Susceptible-Infected-Recovered (SIR)\cite{Kermack1927} and its extensions such as the Susceptible-Exposed-Infected-Recovered (SEIRS)\cite{Ottar2020,Ignazio2021,Grimm2021,Paoluzzi2021} are commonly used to model…

Populations and Evolution · Quantitative Biology 2025-07-14 Kasturi Banerjee , Subhankar Ray , Jayalakshmi Shamanna

We study SIR type epidemics on graphs in two scenarios: (i) when the initial infections start from a well connected central region, (ii) when initial infections are distributed uniformly. Previously, \'Odor et al. demonstrated on a few…

Combinatorics · Mathematics 2023-04-25 Dániel Keliger , László Lovász , Tamás Móri , Gergely Ódor

The SIRS process is a continuous-time process for how infections spread on a graph. In this model, each vertex is in one of the following three states: susceptible (to the infection; S), infected (I), or recovered (R) and thus immune to the…

Probability · Mathematics 2026-05-20 Andreas Göbel , Nicolas Klodt , Martin S. Krejca

Infectious diseases spread through human networks. Susceptible-Infected-Removed (SIR) model is one of the epidemic models to describe infection dynamics on a complex network connecting individuals. In the metapopulation SIR model, each node…

Physics and Society · Physics 2015-08-27 Kanako Mizuno , Kazue Kudo

Stochastic infection processes are continuous-time Markov chains on graphs that assign each vertex one of multiple states, such as susceptible, infected, or recovered. Depending on the model, vertices change their state based on random…

Probability · Mathematics 2026-05-20 Nicolas Klodt , Martin S. Krejca

We investigate a model of a parasite population invading spatially distributed immobile hosts on a graph, which is a modification of the frog model. Each host has an unbreakable immunity against infection with a certain probability $1-p$…

Probability · Mathematics 2026-01-27 Sascha Franck

We are interested in the geometry of the ``infection tree'' in a stochastic SIR (Susceptible-Infectious-Recovered) model, starting with a single infectious individual. This tree is constructed by drawing an edge between two individuals when…

Probability · Mathematics 2025-04-07 Emmanuel Kammerer , Igor Kortchemski , Delphin Sénizergues

In the standard SIR model on a graph, infected vertices infect their neighbors at rate $\alpha$ and recover at rate $\mu$. We consider a two-type SIR process where each individual in the graph can be infected with two types of diseases, $A$…

Probability · Mathematics 2026-02-24 Ruibo Ma , Tai Heng Liu , Baghdadi Othmane , Dong Yao

In this paper, we are concerned with the stochastic susceptible-infectious-susceptible (SIS) epidemic model on the complete graph with $n$ vertices. This model has two parameters, which are the infection rate and the recovery rate. By…

Probability · Mathematics 2020-12-02 Huazheng Bu , Xiaofeng Xue

The susceptible-infectious-recovered (SIR) model describes the evolution of three species of individuals which are subject to an infection and recovery mechanism. A susceptible $S$ can become infectious with an infection rate $\beta$ by an…

Statistical Mechanics · Physics 2008-06-30 Gunter M. Schütz , Marian Brandau , Steffen Trimper

We study the growth of two competing infection types on graphs generated by the configuration model with a given degree sequence. Starting from two vertices chosen uniformly at random, the infection types spread via the edges in the graph…

Probability · Mathematics 2017-11-09 Daniel Ahlberg , Maria Deijfen , Svante Janson

Compartmental transmission models have become an invaluable tool to study the dynamics of infectious diseases. The Susceptible-Infectious-Recovered (SIR) model is known to have an exact semi-analytical solution. In the current study, the…

Populations and Evolution · Quantitative Biology 2020-11-03 Kevin Heng , Christian L. Althaus

The contact process, or SIS epidemic, is a continuous-time Markov process used to model the spread of infection on a graph. Each vertex is either healthy or infected, and each infected vertex independently infects each of its healthy…

Probability · Mathematics 2025-12-09 Shirshendu Chatterjee , David Sivakoff , Matthew Wascher

We study the SIRS process, a continuous-time Markov chain modeling the spread of infections on graphs. In this model, vertices are either susceptible, infected, or recovered. Each infected vertex becomes recovered at rate 1 and infects each…

Probability · Mathematics 2022-11-10 Tobias Friedrich , Andreas Göbel , Nicolas Klodt , Martin S. Krejca , Marcus Pappik

The evoSIR model is a modification of the usual SIR process on a graph $G$ in which $S-I$ connections are broken at rate $\rho$ and the $S$ connects to a randomly chosen vertex. The evoSI model is the same as evoSIR but recovery is…

Probability · Mathematics 2023-10-03 Rick Durrett , Dong Yao

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,…

Probability · Mathematics 2020-08-17 Frank Ball , Tom Britton

If we consider the contact process with infection rate $\lambda$ on a random graph on $n$ vertices with power law degree distributions, mean field calculations suggest that the critical value $\lambda_c$ of the infection rate is positive if…

Probability · Mathematics 2009-12-10 Shirshendu Chatterjee , Rick Durrett

In this paper, we focus on the node-based epidemic modeling for networks, introduce the propagation medium and propose a node-based Susceptible-Infected-Recovered-Susceptible (SIRS) epidemic model with infective media. Theoretical…

Physics and Society · Physics 2019-01-03 Leyi Zheng , Longkun Tang

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