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We study the classic Susceptible-Infected-Recovered (SIR) model for the spread of an infectious disease. In this stochastic process, there are two competing mechanism: infection and recovery. Susceptible individuals may contract the disease…

Populations and Evolution · Quantitative Biology 2012-05-08 E. Ben-Naim , P. L. Krapivsky

It is the main purpose of this paper to introduce a graph-valued stochastic process in order to model the spread of a communicable infectious disease. The major novelty of the SIR model we promote lies in the fact that the social network on…

Applications · Statistics 2014-02-06 Charanpal Dhanjal , Stéphan Clémençon

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

The susceptible-infected-recovered (SIR) model and its variants form the foundation of our understanding of the spread of diseases. Here, each agent can be in one of three states (susceptible, infected, or recovered), and transitions…

Disordered Systems and Neural Networks · Physics 2023-12-25 Claudia Merger , Jasper Albers , Carsten Honerkamp , Moritz Helias

We propose a network behavioral-feedback Susceptible-Infected-Recovered (SIR) epidemic model in which the interaction matrix describing the infection rates across subpopulations depends in feedback on the current epidemic state. This model…

Dynamical Systems · Mathematics 2025-07-08 Martina Alutto , Leonardo Cianfanelli , Giacomo Como , Fabio Fagnani

In real social networks, person-to-person interactions are known to be heterogeneous, which can affect the way a disease spreads through a population, reaches a tipping point in the fraction of infected individuals, and becomes an epidemic.…

Physics and Society · Physics 2020-05-12 Ignacio A. Perez , Paul A. Trunfio , Cristian E. La Rocca , Lidia A. Braunstein

We adopt a maximum-likelihood framework to estimate parameters of a stochastic susceptible-infected-recovered (SIR) model with contact tracing on a rooted random tree. Given the number of detectees per index case, our estimator allows to…

Dynamical Systems · Mathematics 2023-11-23 Augustine Okolie , Johannes Müller , Mirjam Kretzschmar

Compartmental epidemic models, grounded in mass-action kinetics, often assume homogeneous mixing. Although this neglects network structure, recent results show that for Poisson random graphs, the classical SIR model, especially the…

Populations and Evolution · Quantitative Biology 2026-04-28 Akshara Bhat , Abhishek Deshpande , Chittaranjan Hens , Subrata Ghosh

Mathematical modeling of disease spreading plays a crucial role in understanding, controlling and preventing epidemic outbreaks. In a microscopic description of the propagation of a disease over the complex network of human contacts, the…

Physics and Society · Physics 2021-10-08 Federico Malizia , Luca Gallo , Mattia Frasca , Vito Latora , Giovanni Russo

We present a stochastic model for two successive SIR (Susceptible, Infectious, Recovered) epidemics in the same network structured population. Individuals infected during the first epidemic might have (partial) immunity for the second one.…

Populations and Evolution · Quantitative Biology 2024-10-29 Frank Ball , Abid Ali Lashari , David Sirl , Pieter Trapman

This paper presents a detailed mathematical investigation into the dynamics of COVID-19 infections through extended Susceptible-Infected-Recovered (SIR) and Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological models. By…

Populations and Evolution · Quantitative Biology 2025-05-21 Caleb Traxler , Minh Ton , Nameer Ahmed , Sasha Prostota , Annie Cheng

In this paper we consider a model for the spread of a stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemic on a network of individuals described by a random intersection graph. Individuals belong to a random number of…

Probability · Mathematics 2014-04-29 Frank G. Ball , David J. Sirl , Pieter Trapman

We study the Susceptible-Infected-Recovered (SIR) and the Susceptible-Exposed-Infected-Recovered (SEIR) models of epidemics, with possibly time-varying rates, on a class of networks that are locally tree-like, which includes sparse…

Probability · Mathematics 2023-09-22 Juniper Cocomello , Kavita Ramanan

Higher-order interactions play an important role in complex contagion processes. Mean-field approximations have been used to characterize the onset of spreading in the presence of group interactions. However, individual-based mean-field…

Physics and Society · Physics 2024-10-02 Federico Malizia , Luca Gallo , Mattia Frasca , István Z. Kiss , Vito Latora , Giovanni Russo

To simplify mathematical models of disease spread, we often assume equal contact rates among hosts, but real-world scenarios differ. Network-based frameworks help capture these complexities and structural variations in actual systems. We…

Dynamical Systems · Mathematics 2024-07-03 Saswata Das , Mohammad Hossein Samaei , Caterina Scoglio

We consider state and parameter estimation for compartmental models having both time-varying and time-invariant parameters. Though the described Bayesian computational framework is general, we look at a specific application to the…

Computational Engineering, Finance, and Science · Computer Science 2023-11-07 Brandon Robinson , Philippe Bisaillon , Jodi D. Edwards , Tetyana Kendzerska , Mohammad Khalil , Dominique Poirel , Abhijit Sarkar

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

The Susceptible-Infected-Recovered (SIR) model has successfully mimicked the propagation of such airborne diseases as influenza A (H1N1). Although the SIR model has recently been studied in a multilayer networks configuration, in almost all…

Physics and Society · Physics 2015-07-16 L. G. Alvarez Zuzek , H. E. Stanley , L. A. Braunstein

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

The SIR-compartment model is among the simplest models that describe the spread of a disease through a population. The model makes the unrealistic assumption that the population through which the disease is spreading is well-mixed. Although…

Populations and Evolution · Quantitative Biology 2022-11-16 Ryan Wilkinson , Marcus Roper