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Public health services are constantly searching for new ways to reduce the spread of infectious diseases, such as public vaccination of asymptomatic individuals, quarantine (isolation) and treatment of symptomatic individuals. Epidemic…

Populations and Evolution · Quantitative Biology 2018-06-11 Shanshan Chen , Michael Small , Xinchu Fu

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 consider the problem of controlling an SIR-model epidemic by temporarily reducing the rate of contact within a population. The control takes the form of a multiplicative reduction in the contact rate of infectious individuals. The…

Optimization and Control · Mathematics 2021-06-29 David I. Ketcheson

Compartmental transmission models have become an invaluable tool to study the dynamics of infectious diseases. The Susceptible-Infectious-Recovered (SIR) model is known to have an exact semi-analytical solution. In the current study, the…

Populations and Evolution · Quantitative Biology 2020-11-03 Kevin Heng , Christian L. Althaus

This paper studies the distribution function of the time of extinction of a subcritical epidemic, when a large enough proportion of the population has been immunized and/or the infectivity of the infectious individuals has been reduced, so…

Probability · Mathematics 2023-04-05 Anicet Mougabe-Peurkor , Ibrahima Drame , Modeste N'zi , Etienne Pardoux

Current modeling of infectious diseases allows for the study of complex and realistic scenarios that go from the population to the individual level of description. However, most epidemic models assume that the spreading process takes place…

Physics and Society · Physics 2015-04-15 Joaquín Sanz , Cheng-Yi Xia , Sandro Meloni , Yamir Moreno

We consider in this paper a general SEIRS model describing the dynamics of an infectious disease including latency, waning immunity and infection-induced mortality. We derive an infinite system of differential equations that provides an…

Optimization and Control · Mathematics 2022-01-26 Marcel Fang , Pierre-Alexandre Bliman

Stochastic models are widely used to investigate the spread of epidemics in a complex environment. This paper extends a deterministic SAIRS epidemic model to a stochastic case with limited patient capacity and exposure. We first study the…

Probability · Mathematics 2024-05-20 Xiaohui Zhang , Zhiming Li , Shenglong Chen , Jikai Yang

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

Infection spread among individuals is modelled with a continuous time Markov chain, in which subject interactions depend on their distance in space. The well known SIR model and non local variants of the latter are then obtained as large…

Probability · Mathematics 2023-09-27 Franco Flandoli , Francesco Grotto , Andrea Papini , Cristiano Ricci

We propose a network behavioral-feedback Susceptible-Infected-Recovered (SIR) epidemic model in which the interaction matrix describing the infection rates across subpopulations depends in feedback on the current epidemic state. This model…

Dynamical Systems · Mathematics 2025-07-08 Martina Alutto , Leonardo Cianfanelli , Giacomo Como , Fabio Fagnani

The main purpose of this paper is to study the Dynamical behaviors of a stochastic SIS epidemic model using mean-reverting inhomogeneous geometric brownian motion process. First we demonstrate the existence of a global-in-time solution and…

Applications · Statistics 2026-04-03 Lahcen Khammich , Driss Kiouach

We propose a mathematical model to analyze the effects of anti-infection behavior on the equilibrium states of an infectious disease. The anti-infection behavior is incorporated into a classical epidemiological SIR model, by considering the…

Populations and Evolution · Quantitative Biology 2020-09-11 Andrés David Báez-Sánchez , Nara Bobko

A class of models of biological population and communities with a singular equilibrium at the origin is analyzed; it is shown that these models can possess a dynamical regime of deterministic extinction, which is crucially important from…

Quantitative Methods · Quantitative Biology 2007-05-23 Faina S Berezovskaya , Artem S Novozhilov , Georgy P Karev

The worldwide spread of COVID-19 has called for fast advancement of new modelling strategies to estimate its unprecedented spread. Here, we introduce a model based on the fundamental SIR equations with a stochastic disorder by a random…

Physics and Society · Physics 2020-04-28 Suman Dutta

We show that the mean field equations for the SIR epidemic can be exactly solved for a network with arbitrary degree distribution. Our exact solution consists of reducing the dynamics to a lone first order differential equation, which has a…

Physics and Society · Physics 2012-06-28 Andrew Lucas

This paper proposes and analyzes a malaria transmission model structured by the chronological age of the human host population. The model couples an age-structured SIRS system for humans, incorporating waning immunity, with an SI system for…

Analysis of PDEs · Mathematics 2026-03-17 Seraphin Djaoue , Quentin Richard , Antoine Perasso , Irépran Damakoa

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

We study fast-slow versions of the SIR, SIRS, and SIRWS epidemiological models. The multiple time scale behavior is introduced to account for large differences between some of the rates of the epidemiological pathways. Our main purpose is…

Dynamical Systems · Mathematics 2021-12-30 Hildeberto Jardón-Kojakhmetov , Christian Kuehn , Andrea Pugliese , Mattia Sensi

This work focuses on feedback control strategies for applying the sterile insect technique (SIT) to eliminate pest populations. The presentation is centered on the case of mosquito populations, but most of the results can be extended to…

Analysis of PDEs · Mathematics 2025-12-03 Kala Agbo Bidi , Luís Almeida , Jean-Michel Coron