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Epidemics generally spread through a succession of waves that reflect factors on multiple timescales. On short timescales, super-spreading events lead to burstiness and overdispersion, while long-term persistent heterogeneity in…

Populations and Evolution · Quantitative Biology 2022-05-04 Alexei V. Tkachenko , Sergei Maslov , Ahmed Elbanna , George N. Wong , Zachary J. Weiner , Nigel Goldenfeld

We study a well mixed SIR epidemic model with heterogeneous susceptibility and infectivity, allowing for an arbitrary joint distribution of these traits. Using an exact final size formulation and a branching process approximation for early…

Populations and Evolution · Quantitative Biology 2026-01-06 Mohamed El Khalifi

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

Multiple viruses are widely studied because of their negative effect on the health of host as well as on whole population. The dynamics of coinfection is important in this case. We formulated a SIR model that describes the coinfection of…

Dynamical Systems · Mathematics 2019-05-14 Samia Ghersheen , Vladimir Kozlov , Vladimir G. Tkachev , Uno Wennergren

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

SIR models, also with age structure, can be used to describe the evolution of an infective disease. A vaccination campaign influences this dynamics immunizing part of the susceptible individuals, essentially turning them into recovered…

Analysis of PDEs · Mathematics 2019-10-17 Rinaldo M. Colombo , Mauro Garavello

In this paper, a susceptible-infected-susceptible (SIS) model with identical infectivity, where each node is assigned with the same capability of active contacts, $A$, at each time step, is presented. We found that on scale-free networks,…

Physics and Society · Physics 2007-05-23 Rui Yang , Jie Ren , Wen-Jie Bai , Tao Zhou , Ming-Feng Zhang , Bing-Hong Wang

We study a discrete Susceptible-Infected-Recovered (SIR) model for the spread of infectious disease on a homogeneous tree and the limit behavior of the model in the case when the tree vertex degree tends to infinity. We obtain the…

Probability · Mathematics 2022-07-08 Alexander Gairat , Vadim Shcherbakov

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

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

We study an individual-based stochastic SIR epidemic model with infection-age dependent infectivity on a large random graph, capturing individual heterogeneity and non-homogeneous connectivity. Each individual is associated with particular…

Probability · Mathematics 2026-02-11 Guodong Pang , Étienne Pardoux , Aurélien Velleret

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

Compartmental models like the Susceptible-Infected-Recovered (SIR)\cite{Kermack1927} and its extensions such as the Susceptible-Exposed-Infected-Recovered (SEIRS)\cite{Ottar2020,Ignazio2021,Grimm2021,Paoluzzi2021} are commonly used to model…

Populations and Evolution · Quantitative Biology 2025-07-14 Kasturi Banerjee , Subhankar Ray , Jayalakshmi Shamanna

We consider an epidemic model of SIR type set on a homogeneous tree and investigate the spreading properties of the epidemic as a function of the degree of the tree, the intrinsic basic reproduction number and the strength of the…

Analysis of PDEs · Mathematics 2021-06-09 Christophe Besse , Grégory Faye

A quantitative COVID-19 model that incorporates hidden asymptomatic patients is developed, and an analytic solution in parametric form is given. The model incorporates the impact of lockdown and resulting spatial migration of population due…

Populations and Evolution · Quantitative Biology 2020-06-02 Shaurya Kaushal , Abhineet Singh Rajput , Soumyadeep Bhattacharya , M. Vidyasagar , Aloke Kumar , Meher K. Prakash , Santosh Ansumali

In this work, we aim to understand the influence of the heterogeneity of infection rates on the Susceptible-Infected-Susceptible (SIS) epidemic spreading. Employing the classic SIS model as the benchmark, we study the influence of the…

Physics and Society · Physics 2016-04-06 Bo Qu , Huijuan Wang

A generalization of Kermack-McKendick model of epidemics to the case of inhomogeneous susceptibility of population is proposed. Some quantitative and qualitative features of epidemic process development in this situation are established.

Adaptation and Self-Organizing Systems · Physics 2008-11-20 E. Sh. Gutshabash , M. M. Brook

Most countries are suffering severely from the ongoing covid-19 pandemic despite various levels of preventive measures. A common question is if and when a country or region will reach herd immunity $h$. The classical herd immunity level…

Populations and Evolution · Quantitative Biology 2020-05-08 Tom Britton , Frank Ball , Pieter Trapman

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

Pairwise models are used widely to model epidemic spread on networks. These include the modelling of susceptible-infected-removed (SIR) epidemics on regular networks and extensions to SIS dynamics and contact tracing on more exotic networks…

Populations and Evolution · Quantitative Biology 2018-09-24 István Z. Kiss , Joel C. Miller , Péter L. Simon