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Related papers: Exact solution of a stochastic SIR model

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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

We study extensions of the classical SIR model of epidemic spread. First, we consider a single population modified SIR epidemics model in which the contact rate is allowed to be an arbitrary function of the fraction of susceptible and…

Dynamical Systems · Mathematics 2021-12-17 Martina Alutto , Giacomo Como , Fabio Fagnani

We study a symmetric two-disease SIR co-infection model on networks in which co-infected individuals recover at a rate distinct from that of single infections. The model explicitly represents all co-infection states and features absorbing…

Statistical Mechanics · Physics 2025-12-22 Gerardo Palafox-Castillo , Ericka Fabiola Vázquez-Alcalá , Arturo Berrones-Santos

In this paper, we develop a node-based approximate model for Markovian contagion dynamics on networks. We prove that our approximate model is exact for SIR (susceptible-infectious-recovered) and SEIR…

Dynamical Systems · Mathematics 2021-08-17 Cameron L. Hall , Bram A. Siebert

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

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 formulate a generalized susceptible exposed infectious recovered (SEIR) model on a graph, describing the population dynamics of an open crowded place with an arbitrary topology. As a sample calculation, we discuss three simple cases,…

Physics and Society · Physics 2020-12-18 Andrea Nava , Alessandro Papa , Marco Rossi , Domenico Giuliano

The SIR model is the cornerstone model for mathematical epidemiology, explaining key epidemic features such as the second-order transition between disease-free and epidemic states, the initial exponential growth of outbreaks or the…

Populations and Evolution · Quantitative Biology 2026-03-20 Santiago Lamata-Otín , Alex Arenas , Jesús Gómez-Gardeñes , David Soriano-Paños

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

In the simple mean-field SIS and SIR epidemic models, infection is transmitted from infectious to susceptible members of a finite population by independent $p-$coin tosses. Spatial variants of these models are proposed, in which finite…

Probability · Mathematics 2009-09-29 Steven P. Lalley

In this paper, we present a susceptible-infected-recovered (SIR) model with individuals wearing facial masks and individuals who do not. The disease transmission rates, the recovering rates and the fraction of individuals who wear masks are…

Physics and Society · Physics 2021-06-01 Duan-Shin Lee , Miao Zhu

In this work, we study the epidemic SIR model on a system which takes into consideration face-to-face interaction networks. This approach has been used as prototype to describe people interactions in different kinds of social organizations…

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

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

In this study, a new and natural way of constructing a stochastic Susceptible-Infected-Susceptible (SIS) model is proposed. This approach is natural in the sense that the disease transmission rate, $\beta$, is substituted with a generic,…

Probability · Mathematics 2025-11-07 Berk Tan Perçin

This paper develops an individual-based stochastic network SIR model for the empirical analysis of the Covid-19 pandemic. It derives moment conditions for the number of infected and active cases for single as well as multigroup epidemic…

Econometrics · Economics 2022-01-05 M. Hashem Pesaran , Cynthia Fan Yang

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

Dynamic properties of spreading infection through a heterogeneous population are studied numerically and analytically using a dynamic variant of Watts and Strogatz Small World Network-based stochastic Susceptible-Exposed-Infectious-Removed…

Populations and Evolution · Quantitative Biology 2019-06-28 O. Mosbah , N. Zekri , M. Mokhtari , S. Sahraoui

Susceptible-Infected-Recovered (SIR) models have been used for decades to understand epidemic outbreak dynamics. We develop an SIR model specifically designed to study the effects of population behavior with respect to health and…

Populations and Evolution · Quantitative Biology 2023-08-03 Jasmin Nunuvero , Angelique Santiago , Moshe Cohen , Anca Radulescu

Throughout human history, epidemics have been a constant presence. Understanding their dynamics is essential to predict scenarios and make substantiated decisions. Mathematical models are powerful tools to describe an epidemic behavior.…

Systems and Control · Electrical Eng. & Systems 2024-07-26 Walter HMendes aselein , Diego Eckhard