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We consider a two-species reaction-diffusion system in one space dimension that is derived from an epidemiological model in a spatially periodic environment with two types of pathogens: the wild type and the mutant. The system is of a…

Analysis of PDEs · Mathematics 2025-01-22 Quentin Griette , Hiroshi Matano

An epidemic model, where the dispersal is approximated by nonlocal diffusion operator and spatial domain has one ?xed boundary and one free boundary, is considered in this paper. Firstly, using some elementary analysis instead of…

Analysis of PDEs · Mathematics 2024-05-08 Lei Li , Mingxin Wang

Disease spreading models such as the ubiquitous SIS compartmental model and its numerous variants are widely used to understand and predict the behaviour of a given epidemic or information diffusion process. A common approach to imbue more…

Dynamical Systems · Mathematics 2025-11-18 Eugene Tan , Michael Small , Shannon D. Algar

Motivated by analogies between the spreading of human-to-human infections and of chemical processes, we develop a comprehensive model that accounts both for infection and for transport. In this analogy, the three different populations of…

Populations and Evolution · Quantitative Biology 2020-12-08 Harisankar Ramaswamy , Assad A Oberai , Yannis C Yortsos

In this study, we present an integro-differential model to simulate the local spread of infections. The model incorporates a standard susceptible-infected-recovered (\textit{SIR}-) model enhanced by an integral kernel, allowing for…

Dynamical Systems · Mathematics 2023-07-24 Moritz Schäfer , Peter Heidrich , Thomas Götz

The identification of which nodes are optimal seeds for spreading processes on a network is a non-trivial problem that has attracted much interest recently. While activity has mostly focused on non-recurrent type of dynamics, here we…

Physics and Society · Physics 2020-07-17 Gaël Poux-Médard , Romualdo Pastor-Satorras , Claudio Castellano

An SIR epidemic model with free boundary is investigated. This model describes the transmission of diseases. The behavior of positive solutions to a reaction-diffusion system in a radially symmetric domain is investigated. The existence and…

Analysis of PDEs · Mathematics 2013-02-05 Kwang Ik Kim , Zhigui Lin , Qunying Zhang

We investigate the long-time dynamics of a SIR epidemic model in the case of a population of pathogens infecting a homogeneous host population. The pathogen population is structured by a genotypic variable. When the initial mass of the…

Dynamical Systems · Mathematics 2023-06-05 Jean-Baptiste Burie , Arnaud Ducrot , Quentin Griette

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

Individual contributions to the spread of an epidemic vary widely due to an individual's location in a social network and their intrinsic ability to spread or contract diseases. While the effect of heterogeneous population structure and…

Populations and Evolution · Quantitative Biology 2026-05-14 Abhay Gupta , Nicholas W. Landry

In this work we study the stability properties of the equilibrium points of deterministic epidemic models with nonconstant population size. Models with nonconstant population have been studied in the past only in particular cases, two of…

Optimization and Control · Mathematics 2022-02-25 Florin Avram , Rim Adenane , Lasko Basnarkov , Gianluca Bianchin , Dan Goreac , Andrei Halanay

This is work in progress. We make it accessible hoping that people might find the idea useful. We propose a discrete, recursive 5-compartment model for the spread of epidemics, which we call {\em SEPIR-model}. Under mild assumptions which…

Populations and Evolution · Quantitative Biology 2020-09-02 Matthias Kreck , Erhard Scholz

We consider a standard \textit{susceptible-infected-susceptible} (SIS) model to study behaviors of steady states of epidemic spreading in small-world networks. Using analytical methods and large scale simulations, we recover the usual…

Physics and Society · Physics 2009-11-11 Xin-Jian Xu , Zhi-Xi Wu , Yong Chen , Ying-Hai Wang

We consider the development of hyperbolic transport models for the propagation in space of an epidemic phenomenon described by a classical compartmental dynamics. The model is based on a kinetic description at discrete velocities of the…

Physics and Society · Physics 2021-04-12 Giulia Bertaglia , Lorenzo Pareschi

The last decade saw the advent of increasingly realistic epidemic models that leverage on the availability of highly detailed census and human mobility data. Data-driven models aim at a granularity down to the level of households or single…

Populations and Evolution · Quantitative Biology 2011-08-10 Nicola Perra , Duygu Balcan , Bruno Gonçalves , Alessandro Vespignani

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

We consider the SEIRS epidemiology model with such features of the COVID-19 outbreak as: abundance of unidentified infected individuals, limited time of immunity and a possibility of vaccination. The control of the pandemic dynamics is…

Populations and Evolution · Quantitative Biology 2026-03-31 J. Ilnytskyi , T. Patsahan

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the…

Statistical Mechanics · Physics 2009-11-07 M. E. J. Newman

The contact process is an emblematic model of a non-equilibrium system, containing a phase transition between inactive and active dynamical regimes. In the epidemiological context, the model is known as the susceptible-infected-susceptible…

Statistical Mechanics · Physics 2023-05-12 Wout Merbis , Clélia de Mulatier , Philippe Corboz

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