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The SIR model is a classical model characterizing the spreading of infectious diseases. This model describes the time-dependent quantity changes among Susceptible, Infectious, and Recovered groups. By introducing space-depend effects such…

Quantitative Methods · Quantitative Biology 2024-09-18 Md Abu Talha , Yongjia Xu , Shan Zhao , Weihua Geng

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 nonstandard finite difference scheme for the Susceptible-Infected-Removed (SIR) continuous model. We prove that our discretized system is dynamically consistent with its continuous counterpart and we derive its exact solution.…

Dynamical Systems · Mathematics 2024-09-17 Márcia Lemos-Silva , Sandra Vaz , Delfim F. M. Torres

This article is concerned with a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Neumann boundary condition, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous and…

Analysis of PDEs · Mathematics 2016-01-21 Fei-Ying Yang , Wan-Tong Li , Liang Zhang

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

Although we have made progress in understanding disease spread in complex systems with non-Poissonian activity patterns, current models still fail to capture the full range of recovery time distributions. In this paper, we propose an…

Social and Information Networks · Computer Science 2025-11-25 Jiexi Tang , Yichao Yao , Meiling Xie , Minyu Feng

This paper is concerned with the well-posedness of a diffusion-reaction system for a Susceptible-Exposed-Infected-Recovered (SEIR) mathematical model. This model is written in terms of four nonlinear partial differential equations with…

Analysis of PDEs · Mathematics 2023-07-26 Ferdinando Auricchio , Pierluigi Colli , Gianni Gilardi , Alessandro Reali , Elisabetta Rocca

Motivated by the ongoing pandemic COVID-19, we propose a closed-loop framework that combines inference from testing data, learning the parameters of the dynamics and optimal resource allocation for controlling the spread of the…

Physics and Society · Physics 2021-04-27 Ashish R. Hota , Jaydeep Godbole , Philip E Paré

Contemporary epidemiological models often involve spatial variation, providing an avenue to investigate the averaged dynamics of individual movements. In this work, we extend a recent model by Vaziry, Kolokolnikov, and Kevrekidis [Royal…

Populations and Evolution · Quantitative Biology 2024-10-01 Maryam Ahmadpoortorkamani , Alexei Cheviakov

A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifurcation analysis of the reaction…

Dynamical Systems · Mathematics 2025-09-12 Wael El Khateeb , Chanaka Kottegoda , Chunhua Shan

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

We introduce and investigate an SIS-type model for the spread of an infectious disease, where the infected population is structured with respect to the different strain of the virus/bacteria they are carrying. Our aim is to capture the…

Analysis of PDEs · Mathematics 2019-03-25 Àngel Calsina , József Z. Farkas

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

In this article, we construct a numerical method for a stochastic version of the Susceptible Infected Susceptible (SIS) epidemic model, expressed by a suitable stochastic differential equation (SDE), by using the semi-discrete method to a…

Numerical Analysis · Mathematics 2023-07-28 Yiannis Kiouvrekis , Ioannis S. Stamatiou

The coronavirus pandemic has rapidly evolved into an unprecedented crisis. The susceptible-infectious-removed (SIR) model and its variants have been used for modeling the pandemic. However, time-independent parameters in the classical…

Populations and Evolution · Quantitative Biology 2020-09-09 Hyokyoung G. Hong , Yi Li

The COVID-19 pandemic highlighted the need to improve the modeling, estimation, and prediction of how infectious diseases spread. SEIR-like models have been particularly successful in providing accurate short-term predictions. This study…

Populations and Evolution · Quantitative Biology 2024-12-31 Jorge P. Zubelli , Jennifer Loria , Vinicius V. L. Albani

Network-based models of epidemic spread have become increasingly popular in recent decades. Despite a rich foundation of such models, few low-dimensional systems for modeling SIS-type diseases have been proposed that manage to capture the…

Dynamical Systems · Mathematics 2021-01-01 Carl Corcoran , Alan Hastings

Diffusion of information in networks is at the core of many problems in AI. Common examples include the spread of ideas and rumors as well as marketing campaigns. Typically, information diffuses at a non-linear rate, for example, if markets…

Probability · Mathematics 2024-12-04 Tobias Friedrich , Andreas Göbel , Nicolas Klodt , Martin S. Krejca , Marcus Pappik

We introduce a kinetic model that couples the movement of a population of individuals with the dynamics of a pathogen in the same population. We consider that transmission occurs when a susceptible and an infectious individual are…

Analysis of PDEs · Mathematics 2026-01-30 Carolina Strecht-Fernandes , Fabio A. C. C. Chalub

The non-population conserving SIR (SIR-NC) model to describe the spread of infections in a community is proposed and studied. Unlike the standard SIR model, SIR-NC does not assume population conservation. Although similar in form to the…

Optimization and Control · Mathematics 2020-11-06 Vivek S. Borkar , D. Manjunath