Related papers: Diffusion-Reaction Epidemic Model with a Free Boun…
We investigate the global behaviour of a SIRI epidemic model with distributed delay and relapse. From the theory of functional differential equations with delay, we prove that the solution of the system is unique, bounded, and positive, for…
This paper introduces a novel hybrid model combining Partial Differential Equations (PDEs) and Ordinary Differential Equations (ODEs) to simulate infectious disease dynamics across geographic regions. By leveraging the spatial detail of…
Recent evidences show that individuals who recovered from COVID-19 can be reinfected. However, this phenomenon has rarely been studied using mathematical models. In this paper, we propose a SEIRE epidemic model to describe the spread of the…
We study a system of reaction-diffusion equations posed on a bounded domain composed of subdomains separated by a connected network with a metric graph structure. The reaction-diffusion dynamics with anisotropic diffusion on the graph edges…
This paper examines an epidemic patch model with mass-action transmission mechanism and asymmetric connectivity matrix. Results on the global dynamics of solutions and the spatial structures of endemic solutions are obtained. In particular,…
In this paper, we propose and analyze a nonlocal cooperative reaction--diffusion system with free boundaries and drift terms, motivated by directional epidemic spread. Lacking a variational structure but requiring sharper regularity of…
We study the global dynamics of a reaction-diffusion SEIR infection model with distributed delay and nonlinear incidence rate. The well-posedness of the proposed model is proved. By means of Lyapunov functionals, we show that the disease…
In the wake of the 2020 COVID-19 epidemic, much work has been performed on the development of mathematical models for the simulation of the epidemic, and of disease models generally. Most works follow the susceptible-infected-removed (SIR)…
A reaction-diffusion model is investigated to understand infective environments in a man-environment-man epidemic model. The free boundary is introduced to describe the expanding front of an infective environment induced by fecally-orally…
We study the global stability issue of the reaction-convection-diffusion cholera epidemic PDE model and show that the basic reproduction number serves as a threshold parameter that predicts whether cholera will persist or become globally…
Objective: COVID-19 has spread worldwide and made a huge influence across the world. Modeling the infectious spread situation of COVID-19 is essential to understand the current condition and to formulate intervention measurements.…
The SIR model is one of the most prototypical compartmental models in epidemiology. Generalizing this ordinary differential equation (ODE) framework into a spatially distributed partial differential equation (PDE) model is a considerable…
The dynamics of an SIS epidemic patch model with asymmetric connectivity matrix is analyzed. It is shown that the basic reproduction number $R_0$ is strictly decreasing with respect to the dispersal rate of the infected individuals, and the…
We propose and study a new model to describe biological invasions constrained on infinite homogeneous one dimensional metric graphs. Our model consists of an infinite PDE-ODE system where, at each vertex of the one-dimensional lattice…
We present an SI epidemic model whereby a continuous variable captures variability in proliferative potential and resistance to infection among susceptibles. The occurrence of heritable, spontaneous changes in these phenotype and the…
This paper is concerned with the long-time dynamics of an epidemic model whose diffusion and reaction terms involve nonlocal effects described by suitable convolution operators, and the epidemic region is represented by an evolving interval…
The dynamics of many epidemic models for infectious diseases that spread in a single host population demonstrate a threshold phenomenon. If the basic reproduction number R0 is below unity, the disease-free equilibrium P0 is globally stable…
In this article, we consider a dynamic epidemiology model for the spread of the COVID-19 infection. Starting from the classical SEIR model, the model is modified so as to better describe characteristic features of the underlying pathogen…
This work concerns the exponential stabilization of underactuated linear homogeneous systems of m parabolic partial differential equations (PDEs) in cascade (reaction-diffusion systems), where only the first state is controlled either…
This paper is concerned with the well-posedness of a diffusion-reaction system for a Susceptible-Exposed-Infected-Recovered (SEIR) mathematical model. This model is written in terms of four nonlinear partial differential equations with…