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We consider evoSIR, a variant of the SIR model, on Erd\H os-Renyi random graphs in which susceptibles with an infected neighbor break that connection at rate $\rho$ and rewire to a randomly chosen individual. We compute the critical…

Probability · Mathematics 2019-01-23 Yufeng Jiang , Remy Kassem , Grayson York , Matthew Junge , Rick Durrett

Stochastic infection processes are continuous-time Markov chains on graphs that assign each vertex one of multiple states, such as susceptible, infected, or recovered. Depending on the model, vertices change their state based on random…

Probability · Mathematics 2026-05-20 Nicolas Klodt , Martin S. Krejca

We analyze the Susceptible-Infected-Recovered-Susceptible (SIRS) process, a continuous-time Markov chain frequently employed in epidemiology to model the spread of infections on networks. In this framework, infections spread as infected…

Probability · Mathematics 2025-08-21 Phuc Lam , Oanh Nguyen , Iris Yang

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

We propose a new model that describes the dynamics of epidemic spreading on connected graphs. Our model consists in a PDE-ODE system where at each vertex of the graph we have a standard SIR model and connexions between vertices are given by…

Analysis of PDEs · Mathematics 2020-11-25 Christophe Besse , Grégory Faye

We study the SIRS process, a continuous-time Markov chain modeling the spread of infections on graphs. In this model, vertices are either susceptible, infected, or recovered. Each infected vertex becomes recovered at rate 1 and infects each…

Probability · Mathematics 2022-11-10 Tobias Friedrich , Andreas Göbel , Nicolas Klodt , Martin S. Krejca , Marcus Pappik

This paper is concerned with the growth rate of SIR (Susceptible-Infectious-Recovered) epidemics with general infectious period distribution on random intersection graphs. This type of graph is characterized by the presence of cliques…

Probability · Mathematics 2025-08-13 Carolina Fransson

We numerically study the dynamics of the SIR disease model on small-world networks by using a large-deviation approach. This allows us to obtain the probability density function of the total fraction of infected nodes and of the maximum…

Physics and Society · Physics 2022-09-01 Yannick Feld , Alexander K. Hartmann

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

Infectious diseases spread through human networks. Susceptible-Infected-Removed (SIR) model is one of the epidemic models to describe infection dynamics on a complex network connecting individuals. In the metapopulation SIR model, each node…

Physics and Society · Physics 2015-08-27 Kanako Mizuno , Kazue Kudo

In this manuscript, we develop a mobility-based Susceptible-Infectious-Recovered (SIR) model to elucidate the dynamics of pandemic propagation. While traditional SIR models within the field of epidemiology aptly characterize transitions…

Dynamical Systems · Mathematics 2025-01-16 Ciana Applegate , Jiaxu Li , Dan Han

The contact process, or SIS epidemic, is a continuous-time Markov process used to model the spread of infection on a graph. Each vertex is either healthy or infected, and each infected vertex independently infects each of its healthy…

Probability · Mathematics 2025-12-09 Shirshendu Chatterjee , David Sivakoff , Matthew Wascher

We study SIR type epidemics on graphs in two scenarios: (i) when the initial infections start from a well connected central region, (ii) when initial infections are distributed uniformly. Previously, \'Odor et al. demonstrated on a few…

Combinatorics · Mathematics 2023-04-25 Dániel Keliger , László Lovász , Tamás Móri , Gergely Ódor

We propose an extension of the classical susceptible infectious recovered (SIR) model that incorporates the effects of spatial propagation of an epidemic through a small number of additional compartments. The model is designed to capture…

Numerical Analysis · Mathematics 2026-03-02 M. Soledad Aronna , Mariana Bergonzi , Ernesto Kofman

We are interested in predator-prey dynamics on infinite trees, which can informally be seen as particular two-type branching processes where individuals may die (or be infected) only after their parent dies (or is infected). We study two…

Probability · Mathematics 2018-02-19 Igor Kortchemski

We consider an SIR-type (Susceptible $\to$ Infected $\to$ Recovered) stochastic epidemic process with multiple modes of transmission on a contact network. The network is given by a random graph following a multilayer configuration model…

Populations and Evolution · Quantitative Biology 2018-08-22 Karly A. Jacobsen , Mark G. Burch , Joseph H. Tien , Grzegorz A. Rempała

We study the spread of discrete-time epidemics over arbitrary networks for well-known propagation models, namely SIS (susceptible-infected-susceptible), SIR (susceptible-infected-recovered), SIRS (susceptible-infected-recovered-susceptible)…

Social and Information Networks · Computer Science 2016-10-03 Navid Azizan Ruhi , Hyoung Jun Ahn , Babak Hassibi

Becker, Greaves-Tunnell, Kontorovich, Miller, Ravikumar, and Shen determined the long term evolution of virus propagation behavior on a hub-and-spoke graph of one central node and $n$ neighbors, with edges only from the neighbors to the hub…

Dynamical Systems · Mathematics 2022-12-16 Akihiro Takigawa , Steven J. Miller

One of the popular dynamics on complex networks is the epidemic spreading. An epidemic model describes how infections spread throughout a network. Among the compartmental models used to describe epidemics, the…

Physics and Society · Physics 2011-07-14 Faryad Darabi Sahneh , Caterina Scoglio

Compartmental transmission models have become an invaluable tool to study the dynamics of infectious diseases. The Susceptible-Infectious-Recovered (SIR) model is known to have an exact semi-analytical solution. In the current study, the…

Populations and Evolution · Quantitative Biology 2020-11-03 Kevin Heng , Christian L. Althaus