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Related papers: A discrete-time epidemic SISI model

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This paper investigates asymptotic behavior of a stochastic SIR epidemic model, which is a system with degenerate diffusion. It gives sufficient conditions that are very close to the necessary conditions for the permanence. In addition,…

Probability · Mathematics 2015-12-24 N. T. Dieu , D. H. Nguyen , N. H. Du , G. Yin

In this article, we introduce an infinite-dimensional deterministic SIS model which takes into account the heterogeneity of the infections and the social network among a large population. We study the long-time behavior of the dynamic. We…

Dynamical Systems · Mathematics 2020-06-16 Jean-François Delmas , Dylan Dronnier , Pierre-André Zitt

Stochastic modeling of disease dynamics has had a long tradition. Among the first epidemic models including a spatial structure in the form of local interactions is the contact process. In this article we investigate two extensions of the…

Probability · Mathematics 2007-05-23 L. Belhadji , N. Lanchier

Throughout human history, epidemics have been a constant presence. Understanding their dynamics is essential to predict scenarios and make substantiated decisions. Mathematical models are powerful tools to describe an epidemic behavior.…

Systems and Control · Electrical Eng. & Systems 2024-07-26 Walter HMendes aselein , Diego Eckhard

Numerous elements drive the spread of infectious diseases in complex real-world networks. Of particular interest is social behaviors that evolve in tandem with the spread of disease. Moreover, recent studies highlight the importance of…

Systems and Control · Electrical Eng. & Systems 2025-10-03 Benjamin Catalano , Keith Paarporn , Sebin Gracy

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

The conceptual difference between equilibrium and non-equilibrium steady state (NESS) is well established in physics and chemistry. This distinction, however, is not widely appreciated in dynamical descriptions of biological populations in…

Populations and Evolution · Quantitative Biology 2012-02-23 Jia-Zeng Wang , Min Qian , Hong Qian

We introduce a stochastic SIR-type partial differential equation model incorporating random diffusion, reinfection, vital dynamics, and a randomly varying transmission rate. For the associated random dynamical system, we prove the existence…

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

We extend our BDI (birth-death-immigration) process based stochastic model of an infectious disease to time-nonhomogeneous cases. First, we discuss the deterministic model, and derive the expected value of the infection process. Then as an…

Methodology · Statistics 2021-01-25 Hisashi Kobayashi

In this paper, we develop a multi-group epidemic framework via virtual dispersal where the risk of infection is a function of the residence time and local environmental risk. This novel approach eliminates the need to define and measure…

Populations and Evolution · Quantitative Biology 2015-04-01 Derdei Bichara , Yun Kang , Carlos Castillo-Chavez , Richard Horan , Charles Perrings

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

In this paper we present a model describing Susceptible-Infected-Susceptible (SIS) type epidemics spreading on a dynamic contact network with random link activation and deletion where link ac- tivation can be locally constrained. We use and…

Dynamical Systems · Mathematics 2015-05-30 Michael Taylor , Timothy J. Taylor , Istvan Z. Kiss

We propose a lattice dynamical system that arises in a discrete diffusive two-group epidemic model with latency in a patchy environment. The model considers the SIS form and latency of the disease in group 1, while the SIR form without…

Populations and Evolution · Quantitative Biology 2024-10-21 Chufen Wu , Yonghui Xia , Jianshe Yu

We formulate a general SEIR epidemic model in a heterogenous population characterized by some trait in a discrete or continuous subset of a space R d. The incubation and recovery rates governing the evolution of each homogenous…

Analysis of PDEs · Mathematics 2023-03-03 Luís Almeida , Pierre-Alexandre Bliman , Grégoire Nadin , Benoît Perthame , Nicolas Vauchelet

The main aim of the work is to present a general class of two time scales discrete-time epidemic models. In the proposed framework the disease dynamics is considered to act on a slower time scale than a second different process that could…

Dynamical Systems · Mathematics 2024-02-07 Luis Sanz-Lorenzo , Rafael Bravo de la Parra

The death toll for Covid-19 may be reduced by dividing the population into two classes, the vulnerable and the fit, with different lockdown regimes. Instead of one reproduction number there now are four parameters. These make it possible to…

Populations and Evolution · Quantitative Biology 2020-10-05 Guus Balkema

This study investigates an SEIS PDE model with a free boundary, which captures the dynamics of epidemic transmission, including diseases like COVID-19. This parabolic PDE system is analyzed in a rotationally symmetric domain, and the…

Analysis of PDEs · Mathematics 2025-11-11 Aesol Jeon , Ki-Ahm Lee

In this paper, an epidemic model with spatial dependence is studied and results regarding its stability and numerical approximation are presented. We consider a generalization of the original Kermack and McKendrick model in which the size…

Numerical Analysis · Mathematics 2022-04-05 Bálint Takács , Yiannis Hadjimichael

The stochastic SIRS model is a continuous-time Markov chain modelling the spread of infectious diseases with temporary immunity, in a homogeneously-mixing population of fixed size $N$. We study the scaling behaviour of the extinction time…

Probability · Mathematics 2021-01-14 Jingran Zhai