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Related papers: Exact Solution to a Dynamic SIR Model

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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

We investigate the global behaviour of a SIRI epidemic model with distributed delay and relapse. From the theory of functional differential equations with delay, we prove that the solution of the system is unique, bounded, and positive, for…

Classical Analysis and ODEs · Mathematics 2019-08-12 Abdelhai Elazzouzi , Abdesslem Lamrani Alaoui , Mouhcine Tilioua , Delfim F. M. Torres

Modeling epidemic dynamics plays an important role in studying how diseases spread, predicting their future course, and designing strategies to control them. In this letter, we introduce a model of SIR (susceptible-infected-removed) type…

Populations and Evolution · Quantitative Biology 2013-12-17 Li Chen , Fakhteh Ghanbarnejad , Weiran Cai , Peter Grassberger

In this paper, the exact analytical solution of the Susceptible-Infected-Recovered (SIR) epidemic model is obtained in a parametric form. By using the exact solution we investigate some explicit models corresponding to fixed values of the…

Populations and Evolution · Quantitative Biology 2014-04-24 Tiberiu Harko , Francisco S. N. Lobo , M. K. Mak

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 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

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 main aim of the work is to present a general class of two time scales discrete-time epidemic models. In the proposed framework the disease dynamics is considered to act on a slower time scale than a second different process that could…

Dynamical Systems · Mathematics 2024-02-07 Luis Sanz-Lorenzo , Rafael Bravo de la Parra

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

The SIR model is used extensively in the field of epidemiology, in particular, for the analysis of communal diseases. One problem with SIR and other existing models is that they are tailored to random or Erdos type networks since they do…

Social and Information Networks · Computer Science 2014-10-22 M. S. S. Khan

An integrable discretization of the SIR model with vaccination is proposed. The conserved quantities of the continuous model are inherited to the discrete model through the discretization, since the discretization is based on the…

Exactly Solvable and Integrable Systems · Physics 2023-03-31 Atsushi Nobe

We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model. Through the use of a normal form coordinate transform, we are able to analytically derive the stochastic center manifold along with the…

Adaptation and Self-Organizing Systems · Physics 2015-05-13 Eric Forgoston , Lora Billings , Ira B. Schwartz

In this paper we study a susceptible infectious recovered (SIR) model with asymptomatic patients, contact tracing and isolation on a configuration network. Using degree based approximation, we derive a system of differential equations for…

Social and Information Networks · Computer Science 2022-12-20 Duan-Shin Lee , Ting-Zhe Liu , Ruhui Zhang , Cheng-Shang Chang

This paper seeks to study the evolution of the COVID-19 pandemic based on daily published data from Worldometer website, using a time-dependent SIR model. Our findings indicate that this model fits well such data, for different chosen…

Populations and Evolution · Quantitative Biology 2023-11-28 Rawan H. Madi , Sophie M. Moufawad , Nabil R. Nassif

The growing literature on the propagation of COVID-19 relies on various dynamic SIR-type models (Susceptible-Infected-Recovered) which yield model-dependent results. For transparency and ease of comparing the results, we introduce a common…

Populations and Evolution · Quantitative Biology 2020-06-19 Christian Gourieroux , Joann Jasiak

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

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

The SIR pandemic model suffers from an unrealistic assumption: The rate of removal from the infectious class of individuals is assumed to be proportional to the number of infectious individuals. This means that a change in the rate of…

Populations and Evolution · Quantitative Biology 2021-02-23 Paul A. Reiser

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 investigate the SIR epidemic on a dynamic inhomogeneous Erd\H{o}s-R\'enyi random graph, in which vertices are of one of $k$ types and in which edges appear and disappear independently of each other. We establish a functional law of large…

Probability · Mathematics 2024-04-22 Yuanfei Huang , Adrian Röllin