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Related papers: Critical asymptotic behaviour in the SIR model

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An epidemic model where disease transmission can occur either through global contacts or through local, nearest neighbor interactions is considered. The classical SIR--model describing the global interactions is extended by adding…

Populations and Evolution · Quantitative Biology 2022-02-02 Thomas Götz

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

The Susceptible-Infectious-Recovered (SIR) equations and their extensions comprise a commonly utilized set of models for understanding and predicting the course of an epidemic. In practice, it is of substantial interest to estimate the…

Applications · Statistics 2025-05-07 Omar Melikechi , Alexander L. Young , Tao Tang , Trevor Bowman , David Dunson , James Johndrow

The susceptible-exposed-infectious-susceptible (SEIS) model is well-known in mathematical epidemiology as a model of infection in which there is a latent period between the moment of infection and the onset of infectiousness. The…

Probability · Mathematics 2015-10-06 Eric Foxall

A class of multiple-timescale asymptotic solutions to the equations of the susceptible-infected-recovered (SIR) model is presented for the case of high basic reproduction number, with the inverse of the latter employed as the expansion…

Populations and Evolution · Quantitative Biology 2025-12-25 Oleg B. Shiryaev

We propose a simple SIR model in order to investigate the impact of various confinement strategies on a most virulent epidemic. Our approach is motivated by the current COVID-19 pandemic. The main hypothesis is the existence of two…

Populations and Evolution · Quantitative Biology 2020-12-30 G. Nakamura , B. Grammaticos , M. Badoual

The Susceptible-Infected-Recovered (SIR) model is the cornerstone of epidemiological models. However, this specification depends on two parameters only, which implies a lack of flexibility and the difficulty to replicate the volatile…

Populations and Evolution · Quantitative Biology 2020-11-17 Christian Gourieroux , Yang Lu

We introduce an interacting particle system that models the spread of an epidemic in terms of heterogeneous diffusive dynamics, rather than exogenous contact and transmission rates at the population level as in classical compartmental…

Probability · Mathematics 2026-05-20 Eliana Fausti , Andreas Sojmark

We consider the Susceptible-Infected-Recovered (SIR) epidemic model on a Euclidean network in one dimension in which nodes at a distance $l$ are connected with probability $P(l) \propto l^{-\delta}$ in addition to nearest neighbors. The…

Physics and Society · Physics 2014-07-04 Abdul Khaleque , Parongama Sen

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

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

The SIR model is a three-compartment model of the time development of an epidemic. After normalizing the dependent variables, the model is a system of two non-linear differential equations for the susceptible proportion $S$ and the infected…

Dynamical Systems · Mathematics 2021-04-27 William G. Faris

We introduce an extension to Kermack and McKendrick's classic susceptible-infected-recovered (SIR) model in epidemiology, whose underlying mechanism of infection consists of individuals attending randomly generated social gatherings. This…

Probability · Mathematics 2024-05-08 Roberto Cortez

Pairwise models are used widely to model epidemic spread on networks. These include the modelling of susceptible-infected-removed (SIR) epidemics on regular networks and extensions to SIS dynamics and contact tracing on more exotic networks…

Populations and Evolution · Quantitative Biology 2018-09-24 István Z. Kiss , Joel C. Miller , Péter L. Simon

Containment measures implemented by some countries to suppress the spread of COVID-19 have resulted in a slowdown of the epidemic characterized by time series of daily infections plateauing over extended periods of time. We prove that such…

Physics and Society · Physics 2020-11-17 Filippo Radicchi , Ginestra Bianconi

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…

Physics and Society · Physics 2012-09-25 L. D. Valdez , P. A. Macri , L. A. Braunstein

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 present an exact analytical solution to a one-dimensional model of the Susceptible-Infected-Recovered (SIR) epidemic type, with infection rates dependent on nearest-neighbor occupations. We use a quantum mechanical approach, transforming…

Statistical Mechanics · Physics 2015-05-30 H. Thomas Williams , Irina Mazilu , Dan Mazilu

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 introduce a modified SIR model with memory for the dynamics of epidemic spreading in a constant population of individuals. Each individual is in one of the states susceptible (${\bf S}$), infected (${\bf I}$) or recovered (${\bf R}$). In…

Populations and Evolution · Quantitative Biology 2022-03-03 Michael Bestehorn , Thomas M. Michelitsch , Bernard A. Collet , Alejandro P. Riascos , Andrzej F. Nowakowski