English
Related papers

Related papers: Large graph limit for an SIR process in random net…

200 papers

We study an individual-based stochastic SIR epidemic model with infection-age dependent infectivity on a large random graph, capturing individual heterogeneity and non-homogeneous connectivity. Each individual is associated with particular…

Probability · Mathematics 2026-02-11 Guodong Pang , Étienne Pardoux , Aurélien Velleret

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the…

Statistical Mechanics · Physics 2009-11-07 M. E. J. Newman

Recent work by Erik Volz [arXiv:0705.2092] has shown how to calculate the growth and eventual decay of an SIR epidemic on a static random network, assuming infection and recovery each happen at constant rates. This calculation allows us to…

Populations and Evolution · Quantitative Biology 2016-09-08 Joel C. Miller

We investigate final outcome properties of an SIR (susceptible $\to$ infective $\to$ recovered) epidemic model defined on a population of large sub-communities in which there is stronger disease transmission within the communities than…

Probability · Mathematics 2024-04-08 Frank Ball , David Sirl , Pieter Trapman

We numerically study the dynamics of the SIR disease model on small-world networks by using a large-deviation approach. This allows us to obtain the probability density function of the total fraction of infected nodes and of the maximum…

Physics and Society · Physics 2022-09-01 Yannick Feld , Alexander K. Hartmann

In this paper, we are concerned with SIR epidemics in a random environment on complete graphs, where every edges are assigned with i.i.d. weights. Our main results give large and moderate deviation principles of sample paths of this model.

Probability · Mathematics 2020-01-22 Xiaofeng Xue , Yumeng Shen

This paper is concerned with the growth rate of SIR (Susceptible-Infectious-Recovered) epidemics with general infectious period distribution on random intersection graphs. This type of graph is characterized by the presence of cliques…

Probability · Mathematics 2025-08-13 Carolina Fransson

A Markovian SIR (Susceptible-Infectious-Recovered) model is considered for the spread of an epidemic on a configuration model network, in which susceptible individuals may take preventive measures by dropping edges to infectious neighbours.…

Probability · Mathematics 2019-01-23 Frank Ball , Tom Britton , Ka Yin Leung , David Sirl

This paper considers a stochastic SIR (susceptible$\to$infective$\to$removed) epidemic model in which individuals may make infectious contacts in two ways, both within `households' (which for ease of exposition are assumed to have equal…

Probability · Mathematics 2015-03-13 Frank Ball , David Sirl , Pieter Trapman

The spread of an infectious disease depends on intrinsic properties of the disease as well as the connectivity and actions of the population. This study investigates the dynamics of an SIR type model which accounts for human tendency to…

Dynamical Systems · Mathematics 2021-07-26 Hannah Scanlon , John Gemmer

Multiple-type branching processes that model the spread of infectious diseases are investigated. In these stochastic processes, the disease goes through multiple stages before it eventually disappears. We mostly focus on the critical…

Populations and Evolution · Quantitative Biology 2015-06-04 Tibor Antal , P. L. Krapivsky

We propose a new model that describes the dynamics of epidemic spreading on connected graphs. Our model consists in a PDE-ODE system where at each vertex of the graph we have a standard SIR model and connexions between vertices are given by…

Analysis of PDEs · Mathematics 2020-11-25 Christophe Besse , Grégory Faye

Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many…

Physics and Society · Physics 2016-12-21 César Parra-Rojas , Thomas House , Alan J. McKane

In the standard SIR model, infected vertices infect their neighbors at rate $\lambda$ independently across each edge. They also recover at rate $\gamma$. In this work we consider the SIR-$\omega$ model where the graph structure itself…

Probability · Mathematics 2025-05-16 Wenze Chen , Yuewen Hou , Dong Yao

We study the diffusion of epidemics on networks that are partitioned into local communities. The gross structure of hierarchical networks of this kind can be described by a quotient graph. The rationale of this approach is that individuals…

Social and Information Networks · Computer Science 2016-01-19 Stefano Bonaccorsi , Stefania Ottaviano , Delio Mugnolo , Francesco De Pellegrini

We consider evoSIR, a variant of the SIR model, on Erd\H os-Renyi random graphs in which susceptibles with an infected neighbor break that connection at rate $\rho$ and rewire to a randomly chosen individual. We compute the critical…

Probability · Mathematics 2019-01-23 Yufeng Jiang , Remy Kassem , Grayson York , Matthew Junge , Rick Durrett

A network epidemic model is studied. The underlying social network has two different types of group structures, households and workplaces, such that each individual belongs to exactly one household and one workplace. The random network is…

Probability · Mathematics 2024-10-10 Frank Ball , Tom Britton , Peter Neal

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…

Physics and Society · Physics 2007-05-23 Rui Yang , Bing-Hong Wang , Jie Ren , Wen-Jie Bai , Zhi-Wen Shi , Wen-Xu Wang , Tao Zhou

We study a discrete Susceptible-Infected-Recovered (SIR) model for the spread of infectious disease on a homogeneous tree and the limit behavior of the model in the case when the tree vertex degree tends to infinity. We obtain the…

Probability · Mathematics 2022-07-08 Alexander Gairat , Vadim Shcherbakov

Mathematical modeling of epidemic propagation on networks is extended to hypergraphs in order to account for both the community structure and the nonlinear dependence of the infection pressure on the number of infected neighbours. The exact…

Dynamical Systems · Mathematics 2016-10-31 Ágnes Bodó , Gyula Y. Katona , Péter L. Simon