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Related papers: Stochastic epidemic SIR models with hidden states

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We study an infection-age structured epidemic model in which both the infectivity and the rate of loss of immunity depend on the time-since-infection. The model can be equivalently viewed as a nonlinear renewal equation for the incidence of…

Dynamical Systems · Mathematics 2025-11-13 Francesca Scarabel , Harry Coldwell , Tyler Cassidy

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 the effect of external infection sources on phase transitions in epidemic processes. In particular, we consider an epidemic spreading on a network via the SIS/SIR dynamics, which in addition is aided by external agents - sources…

Social and Information Networks · Computer Science 2013-12-05 Siddhartha Banerjee , Avhishek Chatterjee , Sanjay Shakkottai

In the simple mean-field SIS and SIR epidemic models, infection is transmitted from infectious to susceptible members of a finite population by independent $p-$coin tosses. Spatial variants of these models are proposed, in which finite…

Probability · Mathematics 2009-09-29 Steven P. Lalley

With the prevalence of COVID-19, the modeling of epidemic propagation and its analyses have played a significant role in controlling epidemics. However, individual behaviors, in particular the self-protection and migration, which have a…

Social and Information Networks · Computer Science 2025-11-25 Yuhan Li , Ziyan Zeng , Minyu Feng , Jürgen Kurths

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

Infectious diseases spread through human networks. Susceptible-Infected-Removed (SIR) model is one of the epidemic models to describe infection dynamics on a complex network connecting individuals. In the metapopulation SIR model, each node…

Physics and Society · Physics 2015-08-27 Kanako Mizuno , Kazue Kudo

Mathematical models are formal and simplified representations of the knowledge related to a phenomenon. In classical epidemic models, a neglected aspect is the heterogeneity of disease transmission and progression linked to the viral load…

Physics and Society · Physics 2022-05-10 Rossella Della Marca , Nadia Loy , Andrea Tosin

The paper presents an algorithm for syndromic surveillance of an epidemic outbreak formulated in the context of stochastic nonlinear filtering. The dynamics of the epidemic is modeled using a generalized compartmental epidemiological model…

Quantitative Methods · Quantitative Biology 2011-10-24 Alex Skvortsov , Branko Ristic

We adapt the article of Forien, Pang, Pardoux and Zotsa: Arxiv preprint Arxiv2210.04667(2022), on epidemic models with varying infectivity and waning immunity, to incorporate the memory of the last infection. To this end, we introduce a…

Probability · Mathematics 2025-05-02 Hélène Guérin , Arsene Brice Zotsa-Ngoufack

Global pandemics, such as the recent COVID-19 crisis, highlight the need for stochastic epidemic models that can capture the randomness inherent in the spread of disease. Such models must be accompanied by methods for estimating parameters…

Quantitative Methods · Quantitative Biology 2026-04-13 Vincent Wieland , Nils Wassmuth , Lorenzo Contento , Martin Kühn , Jan Hasenauer

A simple, but ``classical``, stochastic model for epidemic spread in a finite, but large, population is studied. The progress of the epidemic can be divided into three different phases that requires different tools to analyse. Initially the…

Populations and Evolution · Quantitative Biology 2018-05-29 Åke Svensson

We investigate final outcome properties of an SIR (susceptible $\to$ infective $\to$ recovered) epidemic model defined on a population of large sub-communities in which there is stronger disease transmission within the communities than…

Probability · Mathematics 2024-04-08 Frank Ball , David Sirl , Pieter Trapman

We study a stochastic epidemic model consisting of elements (organisms in a community or cells in tissue) with fixed positions, in which damage or disease is transmitted by diffusing agents ("signals") emitted by infected individuals. The…

Populations and Evolution · Quantitative Biology 2015-06-05 Fernando P. Faria , Ronald Dickman

Two factors that are often ignored but could play a crucial role in the progression of an infectious disease are the distributions of inherent susceptibility ($\sigma_{inh}$) and external infectivity ($\iota_{ext}$), in a given population.…

Populations and Evolution · Quantitative Biology 2021-01-01 Saumyak Mukherjee , Sayantan Mondal , Biman Bagchi

Health-policy planning requires evidence on the burden that epidemics place on healthcare systems. Multiple, often dependent, datasets provide a noisy and fragmented signal from the unobserved epidemic process including transmission and…

Applications · Statistics 2024-09-11 Alice Corbella , Anne M Presanis , Paul J Birrell , Daniela De Angelis

An SEIRS epidemic with disease fatalities is introduced in a growing population (modelled as a super-critical linear birth and death process). The study of the initial phase of the epidemic is stochastic, while the analysis of the major…

Populations and Evolution · Quantitative Biology 2017-03-29 Tom Britton , Désiré Ouédraogo

Some recent works reveal that there are models of differential equations for the mean and variance of infected individuals that reproduce the SIS epidemic model at some point. This stochastic SIS epidemic model can be interpreted as a…

Populations and Evolution · Quantitative Biology 2020-08-07 Oğul Esen , Eduardo Fernández-Saiz , Cristina Sardón , Marcin Zając

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 study a class of SIRS epidemic dynamical models with a general non-linear incidence rate and transfer from infectious to susceptible. The incidence rate includes a wide range of monotonic, con- cave incidence rates and some non-monotonic…

Dynamical Systems · Mathematics 2017-07-21 Angel G. Cervantes-Pérez , Eric J. Avila-Vales