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Related papers: Exact solution of a stochastic SIR model

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The viral load is known to be a chief predictor of the risk of transmission of infectious diseases. In this work, we investigate the role of the individuals' viral load in the disease transmission by proposing a new…

Adaptation and Self-Organizing Systems · Physics 2023-03-29 Rossella Della Marca , Nadia Loy , Andrea Tosin

We propose a compartmental model for a disease with temporary immunity and secondary infections. From our assumptions on the parameters involved in the model, the system naturally evolves in three time scales. We characterize the equilibria…

Dynamical Systems · Mathematics 2024-04-10 Panagiotis Kaklamanos , Andrea Pugliese , Mattia Sensi , Sara Sottile

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

The Susceptible-Exposed-Infectious-Recovered (SEIR) model is applied in several countries to ascertain the spread of the coronavirus disease 2019 (COVID-19). We consider discrete-time SEIR epidemic model in a closed system which does not…

Dynamical Systems · Mathematics 2021-05-04 U. A. Rozikov , S. K. Shoyimardonov

Stochastic infection processes are continuous-time Markov chains on graphs that assign each vertex one of multiple states, such as susceptible, infected, or recovered. Depending on the model, vertices change their state based on random…

Probability · Mathematics 2026-05-20 Nicolas Klodt , Martin S. Krejca

In the standard SIR model on a graph, infected vertices infect their neighbors at rate $\alpha$ and recover at rate $\mu$. We consider a two-type SIR process where each individual in the graph can be infected with two types of diseases, $A$…

Probability · Mathematics 2026-02-24 Ruibo Ma , Tai Heng Liu , Baghdadi Othmane , Dong Yao

We study the SIR epidemiological model, with a variable contagion rate, applied to the evolution of COVID19 in Cuba. It is highlighted that an increase in the predictive character depends on understanding the dynamics for the temporal…

Populations and Evolution · Quantitative Biology 2020-04-24 Nana Cabo Bizet , Alejandro Cabo Montes de Oca

Consider a Markovian SIR epidemic model in a homogeneous community. To this model we add a rate at which individuals are tested, and once an infectious individual tests positive it is isolated and each of their contacts are traced and…

Populations and Evolution · Quantitative Biology 2022-08-08 Dongni Zhang , Tom Britton

The adoption of prophylaxis attitudes, such as social isolation and use of face masks, to mitigate epidemic outbreaks strongly depends on the support of the population. In this work, we investigate a susceptible-infected-recovered (SIR)…

Physics and Society · Physics 2022-10-05 Diogo H. Silva , Celia Anteneodo , Silvio C. Ferreira

We propose a simple SIR model in order to investigate the impact of various confinement strategies on a most virulent epidemic. Our approach is motivated by the current COVID-19 pandemic. The main hypothesis is the existence of two…

Populations and Evolution · Quantitative Biology 2020-12-30 G. Nakamura , B. Grammaticos , M. Badoual

An SIR model with the coinfection of the two infectious agents in a single host population is considered. The model includes the environmental carry capacity in each class of population. A special case of this model is analyzed and several…

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

We consider a SIRD epidemic model for a population composed of two groups of individuals with asymmetric interactions, where the force of infection depends on the active (alive) population in each group, rather than on the total population,…

Populations and Evolution · Quantitative Biology 2026-01-23 Alison M. V. D. L. Melo , Matheus C. Santos

A simple analytical model for modeling the evolution of the 2020 COVID-19 pandemic is presented. The model is based on the numerical solution of the widely used Susceptible-Infectious-Removed (SIR) populations model for describing…

Populations and Evolution · Quantitative Biology 2020-08-26 Efthimios Kaxiras , George Neofotistos , Eleni Angelaki

We develop an extension of the Susceptible-Infected-Recovery (SIR) model to account for spatial variations in population as well as infection and recovery parameters. The equations are derived by taking the continuum limit of discrete…

Mesoscale and Nanoscale Physics · Physics 2025-02-04 Abhimanyu Ghosh

Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR…

Populations and Evolution · Quantitative Biology 2012-02-28 Artem S Novozhilov

We investigate an epidemic model based on Bailey's continuous differential system. In the continuous time domain, we extend the classical model to time-dependent coefficients and present an alternative solution method to Gleissner's…

Classical Analysis and ODEs · Mathematics 2019-01-01 Martin Bohner , Sabrina Streipert , Delfim F. M. Torres

This paper presents a novel time-space SIR (Susceptible-Infected-Recovered) model for simulating infectious disease dynamics in two interconnected regions. The model is formulated as a coupled reaction-diffusion system with boundary…

Analysis of PDEs · Mathematics 2026-05-13 Omar Elamraoui , Jawad Salhi , Abderrahim Zafrar

An integrable discretization of the SIR model with vaccination is proposed. The conserved quantities of the continuous model are inherited to the discrete model through the discretization, since the discretization is based on the…

Exactly Solvable and Integrable Systems · Physics 2023-03-31 Atsushi Nobe

We investigate the time-evolution and steady states of the stochastic susceptible-infected-recovered-susceptible(SIRS) epidemic model on one- and two- dimensional lattices. We compare the behavior of this system, obtained from computer…

Populations and Evolution · Quantitative Biology 2009-11-10 Jaewook Joo , Joel L. Lebowitz

Many disease models focus on characterizing the underlying transmission mechanism but make simple, possibly naive assumptions about how infections are reported. In this note, we use a simple deterministic Susceptible-Infected-Removed (SIR)…

Populations and Evolution · Quantitative Biology 2019-11-28 Sang Woo Park , Benjamin M. Bolker