Journal ArticleDOI
A reaction-diffusion SIS epidemic model in a time-periodic environment
TLDR
In this paper, the authors considered a susceptible-infected-susceptible (SIS) reaction-diffusion model, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous and temporally periodic and the total population number is constant.Abstract:
In this paper, we consider a susceptible–infected–susceptible (SIS) reaction–diffusion model, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous and temporally periodic and the total population number is constant. We introduce a basic reproduction number and establish threshold-type results on the global dynamics in terms of . In particular, we obtain the asymptotic properties of with respect to the diffusion rate dI of the infected individuals, which exhibit the delicate influence of the time-periodic heterogeneous environment on the extinction and persistence of the infectious disease. Our analytical results suggest that the combination of spatial heterogeneity and temporal periodicity tends to enhance the persistence of the disease.read more
Citations
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Journal ArticleDOI
Basic Reproduction Numbers for Reaction-Diffusion Epidemic Models
Wendi Wang,Xiao-Qiang Zhao +1 more
TL;DR: The basic reproduction number and its computation formulae are established for reaction-diffusion epidemic models with compartmental structure and are applied to a spatial model of rabies to study the influence of spatial heterogeneity and population mobility on disease transmission.
Journal ArticleDOI
A spatial SIS model in advective heterogeneous environments
TL;DR: In this article, the effects of diffusion and advection for a susceptible-infected-susceptible epidemic reaction-diffusion model in heterogeneous environments were studied, and the definition of the basic reproduction number R 0 was given.
Journal ArticleDOI
Dynamics and asymptotic profiles of steady states of an epidemic model in advective environments
TL;DR: In this article, the authors studied the dynamics of a SIS epidemic model of reaction diffusion-advection type and found that the persistence of infected and susceptible populations and the global stability of the disease free equilibrium are established when the basic reproduction number is greater than or less than or equal to one, respectively.
Journal ArticleDOI
A SIS reaction–diffusion–advection model in a low-risk and high-risk domain ☆
TL;DR: In this article, a simplified SIS model is proposed and investigated to understand the impact of spatial heterogeneity of environment and advection on the persistence and eradication of an infectious disease.
Journal ArticleDOI
Asymptotic profiles of steady states for a diffusive SIS epidemic model with mass action infection mechanism
Yixiang Wu,Xingfu Zou,Xingfu Zou +2 more
TL;DR: In this paper, a diffusive SIS model with the mass action infection was considered, and the authors explored the asymptotic profiles of the endemic steady state for small and large diffusion rates.
References
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Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
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Perturbation theory for linear operators
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
Journal ArticleDOI
Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
TL;DR: A precise definition of the basic reproduction number, R0, is presented for a general compartmental disease transmission model based on a system of ordinary differential equations and it is shown that, if R0<1, then the disease free equilibrium is locally asymptotically stable; whereas if R 0>1,Then it is unstable.
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Geometric Theory of Semilinear Parabolic Equations
TL;DR: The neighborhood of an invariant manifold near an equilibrium point is a neighborhood of nonlinear parabolic equations in physical, biological and engineering problems as mentioned in this paper, where the neighborhood of a periodic solution is defined by the invariance of the manifold.