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A Markovian SIR (Susceptible-Infectious-Recovered) model is considered for the spread of an epidemic on a configuration model network, in which susceptible individuals may take preventive measures by dropping edges to infectious neighbours.…

Probability · Mathematics 2019-01-23 Frank Ball , Tom Britton , Ka Yin Leung , David Sirl

We investigate what structural aspects of a collection of twelve empirical temporal networks of human contacts are important to disease spreading. We scan the entire parameter spaces of the two canonical models of infectious disease…

Populations and Evolution · Quantitative Biology 2014-05-27 Petter Holme , Fredrik Liljeros

We consider a very general stochastic model for an SIR epidemic on a network which allows an individual's infectious period, and the time it takes to contact each of its neighbours after becoming infected, to be correlated. We write down…

Populations and Evolution · Quantitative Biology 2017-04-27 Robert R. Wilkinson , Frank G. Ball , Kieran J. Sharkey

We present a class of SEIR Markov chain models for infectious diseases observed over discrete time in a random human population living in a closed environment. The population changes over time through random births, deaths, and transitions…

Populations and Evolution · Quantitative Biology 2019-07-30 Divine Wanduku , Chinmoy Rahul

The Susceptible-Infectious-Recovered (SIR) model is the canonical model of epidemics of infections that make people immune upon recovery. Many of the open questions in computational epidemiology concern the underlying contact structure's…

Physics and Society · Physics 2021-06-09 Petter Holme

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 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

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 propose a new network-based SIR epidemic model in which transmission is modulated by a curvature-weighted contact matrix that encodes structural and geometric features of the underlying graph. The formulation encompasses both…

Dynamical Systems · Mathematics 2025-12-29 Marcilio Ferreira dos Santos

We investigate the expected time to extinction in the susceptible-infectious-susceptible (SIS) model of disease spreading. Rather than using stochastic simulations, or asymptotic calculations in network models, we solve the extinction time…

Populations and Evolution · Quantitative Biology 2018-12-26 Petter Holme , Liubov Tupikina

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

This paper provides an additional probabilistic interpretation of the limiting functions for the SIR epidemic on the configuration model derived in the paper by Janson, Luczak and Windridge (2014).

Probability · Mathematics 2021-04-19 Malwina Luczak

We study the stochastic susceptible-infected-recovered (SIR) model with time-dependent forcing using analytic techniques which allow us to disentangle the interaction of stochasticity and external forcing. The model is formulated as a…

Populations and Evolution · Quantitative Biology 2010-11-23 Andrew J Black , Alan J McKane

We study a stochastic SIS (susceptible-infected-susceptible) epidemic dynamics on network, under the effect of a Markovian regime-switching. We first prove the existence of a unique global positive solution, and find a positive invariant…

Probability · Mathematics 2023-01-03 Stefania Ottaviano , Stefano Bonaccorsi

We study the spread of an SIRS-type epidemic with vaccination on network. Starting from an exact Markov description of the model, we investigate the mean epidemic lifetime by providing a sufficient condition for fast extinction that depends…

Dynamical Systems · Mathematics 2020-11-23 Stefania Ottaviano , Stefano Bonaccorsi

Contact patterns in populations fundamentally influence the spread of infectious diseases. Current mathematical methods for epidemiological forecasting on networks largely assume that contacts between individuals are fixed, at least for the…

Populations and Evolution · Quantitative Biology 2007-05-23 Erik Volz , Lauren Ancel Meyers

This paper is concerned with a stochastic model for the spread of an SEIR (susceptible -> exposed (=latent) -> infective -> removed) epidemic with a contact tracing scheme, in which removed individuals may name some of their infectious…

Probability · Mathematics 2015-12-08 Frank G Ball , Edward S Knock , Philip D O'Neill

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

Most epidemic models assume equal mixing among members of a population. An alternative approach is to model a population as random network in which individuals may have heterogeneous connectivity. This paper builds on previous research by…

Physics and Society · Physics 2007-05-23 Erik Volz

Over the years numerous models of SIS (susceptible - infected - susceptible) disease dynamics unfolding on networks have been proposed. Here, we discuss the links between many of these models and how they can be viewed as more general…

Populations and Evolution · Quantitative Biology 2013-04-10 Timothy J Taylor , Istvan Z Kiss