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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-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

The non-population conserving SIR (SIR-NC) model to describe the spread of infections in a community is proposed and studied. Unlike the standard SIR model, SIR-NC does not assume population conservation. Although similar in form to the…

Optimization and Control · Mathematics 2020-11-06 Vivek S. Borkar , D. Manjunath

We study the problem of optimal control of the stochastic SIR model. Models of this type are used in mathematical epidemiology to capture the time evolution of highly infectious diseases such as COVID-19. Our approach relies on…

Populations and Evolution · Quantitative Biology 2020-05-04 Andrew Lesniewski

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

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

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

Real-time vaccination following an outbreak can effectively mitigate the damage caused by an infectious disease. However, in many cases, available resources are insufficient to vaccinate the entire at-risk population, logistics result in…

Populations and Evolution · Quantitative Biology 2016-03-29 Chantal Nguyen , Jean M. Carlson

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

This paper analyses the optimal control of infectious disease propagation using a classic susceptible-infected-recovered (SIR) model characterised by permanent immunity and the absence of available vaccines. The control is performed over a…

Optimization and Control · Mathematics 2024-06-12 Rocío Balderrama , Mariana Inés Prieto , Constanza Sánchez de la Vega , Federico Vazquez

This paper presents a simple continuous-time linear vaccination-based control strategy for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model. The model takes into account the total…

Dynamical Systems · Mathematics 2011-03-28 M. De la Sen , A. Ibeas , S. Alonso-Quesada

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 the recent COVID-19 pandemic we assisted at a sequence of epidemic waves intertwined by anomalous fade-outs with periods of low but persistent epidemic prevalence. These long-living epidemic states complicate epidemic control and…

Physics and Society · Physics 2025-08-27 Javier Aguilar , Beatriz Arregui García , Raúl Toral , Sandro Meloni , Jose J. Ramasco

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

We consider the SIR epidemiological model applied to the evolution of COVID-19 with two approaches. In the first place we fit a global SIR model, with time delay, and constant parameters throughout the outbreak, including the contagion…

Populations and Evolution · Quantitative Biology 2020-06-23 Nana Geraldine Cabo Bizet , Damián Kaloni Mayorga Peña

We study the susceptible-infective-recovered (SIR) epidemic on a random graph chosen uniformly subject to having given vertex degrees. In this model infective vertices infect each of their susceptible neighbours, and recover, at a constant…

Probability · Mathematics 2014-09-24 Svante Janson , Malwina Luczak , Peter Windridge

To better describe the spread of a disease, we extend a discrete time stochastic SIR-type epidemic model of Tuckwell and Williams. We assume the dependence on time of the number of daily encounters and include a parameter to represent a…

Populations and Evolution · Quantitative Biology 2022-09-30 Mireia Besalú , Giulia Binotto

In this paper, we propose a Susceptible-Infected-Removal (SIR) model with time fused coefficients. In particular, our proposed model discovers the underlying time homogeneity pattern for the SIR model's transmission rate and removal rate…

Applications · Statistics 2021-03-11 Hou-Cheng Yang , Yishu Xue , Yuqing Pan , Qingyang Liu , Guanyu Hu

In this paper we generalise a simple discrete time stochastic SIR type model defined by Tuckwell and Williams. The SIR model by Tuckwell and Williams assumes a homogeneous population, a fixed infectious period, and a strict transition from…

Populations and Evolution · Quantitative Biology 2025-04-21 Carles Rovira

We consider a susceptible, infected, removed (SIR) system where the transmission rate may be temporarily reduced for a fixed amount of time. We show that in order to minimize the total number of fatalities, the transmission rate should be…

Dynamical Systems · Mathematics 2021-07-20 Yuanyuan Feng , Gautam Iyer , Lei Li