English
Related papers

Related papers: Diffusion-Reaction Epidemic Model with a Free Boun…

200 papers

This work examines the dynamics of solutions of a two-strain SIS epidemic model in patchy environments. The basic reproduction number $\mathcal{R}_0$ is introduced, and sufficient conditions are provided to guarantee the global stability of…

Analysis of PDEs · Mathematics 2023-09-12 Jonas T. Doumatè , Tahir B. Issa , Rachidi B. Salako

We study a diffusive SIS epidemic model with the mass-action transmission mechanism and show, under appropriate assumptions on the parameters, the existence of multiple endemic equilibria (EE). Our results answer some open questions on…

Analysis of PDEs · Mathematics 2023-11-07 Keoni Castellano , Rachidi B. Salako

The review is devoted to analysis of mathematical models used for describing epidemic processes. A main focus is done on the models that are based on partial differential equations (PDEs), especially those that were developed and used for…

Populations and Evolution · Quantitative Biology 2024-03-01 Vasyl' Davydovych , Vasyl' Dutka , Roman Cherniha

The interplay between disease spreading and personal risk perception is of key importance for modelling the spread of infectious diseases. We propose a planar system of ordinary differential equations (ODEs) to describe the co-evolution of…

Dynamical Systems · Mathematics 2023-05-09 Massimo A. Achterberg , Mattia Sensi

We study the spreading speed of a diffusive epidemic model proposed by Li et al. \cite{LL}, where the Stefan boundary condition is imposed at the right boundary, and the left boundary is subject to the homogeneous Dirichlet and Neumann…

Analysis of PDEs · Mathematics 2024-07-15 Xueping Li , Lei Li , Mingxin Wang

In this paper, we study an analytically tractable SIS model with a non-linear incidence rate for the number of infectious individuals described through a stochastic differential equation (SDE). We guarantee the existence of a positive…

Probability · Mathematics 2024-04-23 J. S. Builes , Cristian F. Coletti , Leon A. Valencia

We propose a competitive bi-virus model with dynamic social distancing behavior. Our model illustrates how public perception of different viruses changes the conditions for their eradication, their coexistence, or the dominance of one over…

Systems and Control · Electrical Eng. & Systems 2026-05-07 Benjamin Catalano , Keith Paarporn , Sebin Gracy

We consider an epidemic model with nonlocal diffusion and free boundaries, which describes the evolution of an infectious agents with nonlocal diffusion and the infected humans without diffusion, where humans get infected by the agents, and…

Analysis of PDEs · Mathematics 2019-12-06 Meng Zhao , Yang Zhang , Wan-Tong Li , Yihong Du

Networked epidemic models have been widely adopted to describe propagation phenomena. The endemic equilibrium of these models is of great significance in the field of viral marketing, innovation dissemination, and information diffusion.…

Systems and Control · Electrical Eng. & Systems 2020-01-22 Fangzhou Liu , Shaoxuan Cui , Xianwei Li , Martin Buss

We study a nonlocal SIS epidemic model with free boundaries, advection, and spatial heterogeneity, where the dispersal kernels are not assumed to be symmetric. The model describes the evolution of susceptible and infected populations in a…

Analysis of PDEs · Mathematics 2026-03-26 Soufiane Bentout , Hoang-Hung Vo

In this paper, we consider a compartmental SIRS epidemic model with asymptomatic infection and seasonal succession, which is a periodic discontinuous differential system. The basic reproduction number $\mathcal{R}_0$ is defined and valuated…

Dynamical Systems · Mathematics 2017-08-15 Yilei Tang , Dongmei Xiao , Weinian Zhang , Di Zhu

In this paper, we investigate a parabolic-ODE SIS epidemic model with no-flux boundary conditions in a heterogeneous environment. The model incorporates a saturated infection mechanism \({SI}/(m(x) + S + I)\) with \(m \geq,\,\not\equiv 0\).…

Analysis of PDEs · Mathematics 2025-03-28 Rui Peng , Rachidi Salako , Yixiang Wu

We show that the basic reproduction number of an SIS patch model with standard incidence is either strictly decreasing and strictly convex with respect to the diffusion coefficient of infected subpopulation if the patch reproduction numbers…

Populations and Evolution · Quantitative Biology 2020-01-03 Daozhou Gao , Chao-Ping Dong

To study the influence of the moving front of the infected interval and the spatial movement of individuals on the spreading or vanishing of infectious disease, we consider a nonlocal SIS (susceptible-infected-susceptible)…

Analysis of PDEs · Mathematics 2023-01-31 Yachun Tong , Inkyung Ahn , Zhigui Lin

This paper investigates the long-time dynamics of a nonlocal epidemic model with free boundaries, where a pathogen with density $u(t,x)$ and the infected humans with density $v(t,x)$ evolve according to a reaction-diffusion system with…

Analysis of PDEs · Mathematics 2026-02-06 Yao Chen , Yihong Du , Wan-Tong Li , Rong Wang

Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model…

Statistical Mechanics · Physics 2026-03-24 Valentin Anfray , Hong-Yan Shih

A configuration model for epidemic spread, based on a scale-free network, is introduced. We obtain the analytical solutions describing both unstable and stable dynamics of the epidemic spreading, and demonstrate how these regimes can…

Physics and Society · Physics 2020-07-15 Alexander I Nesterov , Pablo Héctor Mata Villafuerte , Gennady P Berman

This paper introduces a nonstandard finite difference (NSFD) approach to a reaction-diffusion SEIQR epidemiological model, which captures the spatiotemporal dynamics of infectious disease transmission. Formulated as a system of semilinear…

Quantitative Methods · Quantitative Biology 2026-05-20 Achraf Zinihi , Matthias Ehrhardt , Moulay Rchid Sidi Ammi

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 consider the SEIRS compartment epidemiology model suitable for predicting the evolution of the COVID-19 pandemy in the extreme limiting case of no acquired immunity. The disease-free and endemic fixed points are found and their stability…

Populations and Evolution · Quantitative Biology 2020-12-15 J. M. Ilnytskyi