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Related papers: SIR model on one dimensional small world networks

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We extend the classical Susceptible-Infected-Recovered (SIR) model to a network-based framework where the degree distribution of nodes follows a Poisson distribution. This extension incorporates an additional parameter representing the mean…

Populations and Evolution · Quantitative Biology 2025-01-03 Josephine K. Wairimu , Andrew Gothard , Grzegorz A. Rempala

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

This paper presents a novel time-space SIR (Susceptible-Infected-Recovered) model for simulating infectious disease dynamics in two interconnected regions. The model is formulated as a coupled reaction-diffusion system with boundary…

Analysis of PDEs · Mathematics 2026-05-13 Omar Elamraoui , Jawad Salhi , Abderrahim Zafrar

We study seasonal epidemic spreading in a susceptible-infected-removed-susceptible (SIRS) model on smallworld graphs. We derive a mean-field description that accurately captures the salient features of the model, most notably a phase…

Statistical Mechanics · Physics 2021-03-26 Daniel Malz , Andrea Pizzi , Andreas Nunnenkamp , Johannes Knolle

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

The disease spreading on complex networks is studied in SIR model. Simulations on empirical complex networks reveal two specific regimes of disease spreading: local containment and epidemic outbreak. The variables measuring the extent of…

Physics and Society · Physics 2013-04-02 Alen Lancic , Nino Antulov-Fantulin , Mile Sikic , Hrvoje Stefancic

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…

Probability · Mathematics 2020-03-10 Monia Capanna

This paper is concerned with stochastic SIR and SEIR epidemic models on random networks in which individuals may rewire away from infected neighbors at some rate $\omega$ (and reconnect to non-infectious individuals with probability…

Populations and Evolution · Quantitative Biology 2016-11-15 Tom Britton , David Juher , Joan Saldana

This paper investigates a behavioral-feedback SIR model in which the infection rate adapts dynamically based on the fractions of susceptible and infected individuals. We introduce an invariant of motion and we characterize the peak of…

Populations and Evolution · Quantitative Biology 2025-09-17 Martina Alutto , Leonardo Cianfanelli , Giacomo Como , Fabio Fagnani , Francesca Parise

The standard pair approximation equations (PA) for the Susceptible-Infective-Recovered-Susceptible (SIRS) model of infection spread on a network of homogeneous degree $k$ predict a thin phase of sustained oscillations for parameter values…

Populations and Evolution · Quantitative Biology 2009-07-28 Ganna Rozhnova , Ana Nunes

We analyze two alterations of the standard susceptible-infected-susceptible (SIS) dynamics that preserve the central properties of spontaneous healing and infection capacity of a vertex increasing unlimitedly with its degree. All models…

Physics and Society · Physics 2018-07-19 Wesley Cota , Angélica S. Mata , Silvio C. Ferreira

This brief note highlights a largely overlooked similarity between the SIR ordinary differential equations used for epidemics on the configuration model of a Poisson network and the classical mass-action SIR equations introduced nearly a…

Populations and Evolution · Quantitative Biology 2023-10-24 Grzegorz A. Rempala

Epidemic propagation on networks represents an important departure from traditional massaction models. However, the high-dimensionality of the exact models poses a challenge to both mathematical analysis and parameter inference. By using…

Quantitative Methods · Quantitative Biology 2023-02-07 István Z. Kiss , Luc Berthouze , Wasiur R. KhudaBukhsh

The ability to actually implement epidemic models is a crucial stake for public institutions, as they may be overtaken by the increasing complexity of current models and sometimes tend to revert to less elaborate models such as the SIR. In…

Physics and Society · Physics 2023-12-19 Louis Bremaud , Olivier Giraud , Denis Ullmo

Epidemic spreading and cascading failure are two important dynamical processes over complex networks. They have been investigated separately for a long history. But in the real world, these two dynamics sometimes may interact with each…

Physics and Society · Physics 2015-06-19 Lurong Jiang , Xinyu Jin , Yongxiang Xia , Bo Ouyang , Duanpo Wu

Most real networks are characterized by connectivity patterns that evolve in time following complex, non-Markovian, dynamics. Here we investigate the impact of this ubiquitous feature by studying the Susceptible-Infected-Recovered (SIR) and…

Physics and Society · Physics 2016-01-20 Kaiyuan Sun , Andrea Baronchelli , Nicola Perra

Although we have made progress in understanding disease spread in complex systems with non-Poissonian activity patterns, current models still fail to capture the full range of recovery time distributions. In this paper, we propose an…

Social and Information Networks · Computer Science 2025-11-25 Jiexi Tang , Yichao Yao , Meiling Xie , Minyu Feng

We introduce a kinetic framework for modeling the time evolution of the statistical distributions of the population densities in the three compartments of susceptible, infectious, and recovered individuals, under epidemic spreading driven…

Analysis of PDEs · Mathematics 2025-12-16 Giorgio Martalò , Giuseppe Toscani , Mattia Zanella

Spreading phenomena are ubiquitous in nature and society. For example, disease, rumor, and information spread over underlying social and information networks. It is well known that there is no threshold for epidemic models on scale-free…

Physics and Society · Physics 2016-03-16 Satoru Morita

The classic SIR model of epidemic dynamics is solved completely by quadratures, including a time integral transform expanded in a series of incomplete gamma functions. The model is also generalized to arbitrary time-dependent infection…

Populations and Evolution · Quantitative Biology 2020-10-07 E. Sadurní , G. Luna-Acosta