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Related papers: An SIR epidemic model with free boundary

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Epidemic spread on networks is one of the most studied dynamics in network science and has important implications in real epidemic scenarios. Nonetheless, the dynamics of real epidemics and how it is affected by the underline structure of…

Physics and Society · Physics 2020-09-08 Bnaya Gross , Shlomo Havlin

In this work, we use a new approach to study the spread of an infectious disease. Indeed, we study a SIR epidemic model with variable infectivity, where the individuals are distributed over a compact subset $D$ of $\R^d$. We define…

Probability · Mathematics 2025-11-18 Armand Kanga , Etienne Pardoux

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

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

In most models of the spread of disease over contact networks it is assumed that the probabilities per unit time of disease transmission and recovery from disease are constant, implying exponential distributions of the time intervals for…

Physics and Society · Physics 2010-07-23 Brian Karrer , M. E. J. Newman

In the standard SIR model, infected vertices infect their neighbors at rate $\lambda$ independently across each edge. They also recover at rate $\gamma$. In this work we consider the SIR-$\omega$ model where the graph structure itself…

Probability · Mathematics 2025-05-16 Wenze Chen , Yuewen Hou , Dong Yao

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

It is generally accepted that scale-free networks is prone to epidemic spreading allowing the onset of large epidemics whatever the spreading rate of the infection. In the paper, we show that disease propagation may be suppressed in…

Other Condensed Matter · Physics 2008-03-05 Zhongzhi Zhang , Shuigeng Zhou , Tao Zou , Jihong Guan

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 in this paper a compartmental SIR model for a population distributed in a bounded domain D of $\mathbb{R}^d$, d= 1, 2, or 3. We describe a spatial model for the spread of a disease on a grid of D. We prove two laws of large…

Probability · Mathematics 2020-07-23 M. N'zi , E. Pardoux , T. Yeo

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

This paper considers a susceptible-infected-susceptible (SIS) epidemic reaction-diffusion model with no-flux boundary conditions and varying total population. The interaction of the susceptible and infected people is describe by the…

Analysis of PDEs · Mathematics 2024-12-13 Rui Peng , Rachidi B. Salako , Yixiang Wu

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 study two simple mathematical models of the epidemic. At first, we study the repetitive infection spreading in a simplified SIRS model including the effect of the decay of the acquired immune. The model is an intermediate model of the…

Populations and Evolution · Quantitative Biology 2024-03-13 Hidetsugu Sakaguchi , Keito Yamasaki

We study the qualitative properties of a spatial diffusive heterogeneous SIR model, that appears in mathematical epidemiology to describe the spread of an infectious disease in a population. The model we consider consists in a system of…

Analysis of PDEs · Mathematics 2020-05-15 Romain Ducasse

We consider a multi-species reaction-diffusion system that arises in epidemiology to describe the spread of several strains, or variants, of a disease in a population. Our model is a natural spatial, multi-species, extension of the…

Analysis of PDEs · Mathematics 2022-08-02 Romain Ducasse , Samuel Nordmann

In this paper, we consider a compartmental SIRS epidemic model with asymptomatic infection and seasonal succession, which is a periodic discontinuous differential system. The basic reproduction number $\mathcal{R}_0$ is defined and valuated…

Dynamical Systems · Mathematics 2017-08-15 Yilei Tang , Dongmei Xiao , Weinian Zhang , Di Zhu

In this paper, we consider an optimal distributed control problem for a reaction-diffusion-based SIR epidemic model with human behavioral effects. We develop a model wherein non-pharmaceutical intervention methods are implemented, but a…

Analysis of PDEs · Mathematics 2025-02-11 Marcelo Bongarti , Christian Parkinson , Weinan Wang

The spread of an infectious disease depends on intrinsic properties of the disease as well as the connectivity and actions of the population. This study investigates the dynamics of an SIR type model which accounts for human tendency to…

Dynamical Systems · Mathematics 2021-07-26 Hannah Scanlon , John Gemmer

In a metapopulation network, infectious diseases spread widely because of the travel of individuals. In the present study, we consider a modified metapopulation Susceptible-Infected-Removed (SIR) model with a latent period, which we call…

Physics and Society · Physics 2017-08-02 Kazue Kudo , Kanako Mizuno