Theoretical analysis on a diffusive SIR epidemic model with nonlinear incidence in a heterogeneous environment

DOI10.3934/dcdsb.2018173zbMath1404.35256OpenAlexW2806838729WikidataQ129608393 ScholiaQ129608393MaRDI QIDQ1756893

Fujun Li, Chengxia Lei, Jiang Liu

Publication date: 27 December 2018

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2018173

zbMATH Keywords

asymptotic profileendemic equilibriumheterogeneous environmenta diffusive SIR epidemic modelpersistence /extinction

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Reaction-diffusion equations (35K57) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Population dynamics (general) (92D25) Boundary value problems for second-order elliptic systems (35J57)

Related Items (31)

Hopf bifurcation of a diffusive SIS epidemic system with delay in heterogeneous environment ⋮ Analysis on a diffusive SI epidemic model with logistic source and saturation infection mechanism ⋮ Global attractivity of the equilibria of the diffusive SIR and SEIR epidemic models with multiple parallel infectious stages and nonlinear incidence mechanism ⋮ Qualitative analysis on an SIRS reaction-diffusion epidemic model with saturation infection mechanism ⋮ Dynamics of diffusive nutrient-microorganism model with spatially heterogeneous environment ⋮ Concentration phenomenon of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with spontaneous infection ⋮ Long-time dynamics of a reaction-diffusion system with negative feedback and inhibition ⋮ A reaction–diffusion SIS epidemic model with saturated incidence rate and logistic source ⋮ On a rumor propagation model with spatial heterogeneity ⋮ Novel spatial profiles of some diffusive SIS epidemic models ⋮ Analysis on a diffusive SIS epidemic model with saturated incidence rate and linear source in a heterogeneous environment ⋮ Dynamics and profiles of a diffusive cholera model with bacterial hyperinfectivity and distinct dispersal rates ⋮ A diffusive SIS epidemic model with saturated incidence function in a heterogeneous environment ^* ⋮ Analysis of global stability and asymptotic properties of a cholera model with multiple transmission routes, spatial diffusion and incomplete immunity ⋮ Asymptotic behavior of an SIS reaction-diffusion-advection model with saturation and spontaneous infection mechanism ⋮ Asymptotic profiles of endemic equilibrium of a diffusive SIS epidemic system with nonlinear incidence function in a heterogeneous environment ⋮ Analysis on a diffusive SIRS epidemic model with logistic source and saturated incidence rate ⋮ Dynamics analysis on a chronic epidemic model with diffusion ⋮ Spatiotemporal dynamics analysis and optimal control method for an SI reaction-diffusion propagation model ⋮ A weighted networked SIRS epidemic model ⋮ Global stability of equilibria of a diffusive SEIR epidemic model with nonlinear incidence ⋮ Qualitative analysis on a diffusive SIRS epidemic model with standard incidence infection mechanism ⋮ Qualitative analysis on an SIS epidemic reaction-diffusion model with mass action infection mechanism and spontaneous infection in a heterogeneous environment ⋮ Asymptotic profiles of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with saturated incidence rate ⋮ Qualitative analysis of a diffusive SIR epidemic model with saturated incidence rate in a heterogeneous environment ⋮ Analysis on a diffusive SIS epidemic system with linear source and frequency-dependent incidence function in a heterogeneous environment ⋮ Concentration behavior of endemic equilibrium for a reaction-diffusion-advection SIS epidemic model with mass action infection mechanism ⋮ Deciphering role of inter and intracity human dispersal on epidemic spread via coupled reaction-diffusion models ⋮ Analysis on a diffusive SEI epidemic model with/without immigration of infected hosts ⋮ Bifurcation Analysis of a Diffusive SIR Model with Saturated Treatment in a Heterogeneous Environment ⋮ Asymptotic dynamics of a logistic SIS epidemic reaction-diffusion model with nonlinear incidence rate

Cites Work

• A priori \(L^\infty\) estimates for solutions of a class of reaction-diffusion systems
• Asymptotic profiles of steady states for a diffusive SIS epidemic model with mass action infection mechanism
• Varying total population enhances disease persistence: qualitative analysis on a diffusive SIS epidemic model
• Traveling wave solutions for a diffusive SIS epidemic model
• A SIS reaction-diffusion-advection model in a low-risk and high-risk domain
• Dynamics and asymptotic profiles of steady states of an epidemic model in advective environments
• An SIS patch model with variable transmission coefficients
• Melnikov analysis of chaos in a simple epidemiological model
• An epidemiological model with a delay and a nonlinear incidence rate
• Some epidemiological models with nonlinear incidence
• Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model
• Dynamics of an SIS reaction-diffusion epidemic model for disease transmission
• An SIS infection model incorporating media coverage
• Effect of a protection zone in the diffusive Leslie predator-prey model
• Global stability of the steady states of an SIS epidemic reaction-diffusion model
• Asymptotic profiles of the positive steady state for an SIS epidemic reaction-diffusion model. I
• Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models
• Dynamical behavior of epidemiological models with nonlinear incidence rates
• Large amplitude stationary solutions to a chemotaxis system
• A semilinear parabolic system arising in the theory of superconductivity
• Elliptic partial differential equations of second order
• A Lyapunov function and global properties for \(SIR\) and \(SEIR\) epidemiological models with nonlinear incidence
• A disease transmission model in a nonconstant population
• Diffusion, self-diffusion and cross-diffusion
• Lyapunov functions and global stability for SIR, SIRS, and SIS epidemiological models
• Robust persistence for semidynamical systems.
• Effect of discretization on dynamical behavior of SEIR and SIR models with nonlinear incidence
• Multiparametric bifurcations for a model in epidemiology
• Concentration profile of endemic equilibrium of a reaction-diffusion-advection SIS epidemic model
• Asymptotic profile of the positive steady state for an SIS epidemic reaction-diffusion model: effects of epidemic risk and population movement
• On the effects of migration and spatial heterogeneity on single and multiple species
• A spatial SIS model in advective heterogeneous environments
• Global dynamics of zooplankton and harmful algae in flowing habitats
• Homoclinic orbits in a disease transmission model with nonlinear incidence and nonconstant population
• The Mathematics of Infectious Diseases
• A reaction–diffusion SIS epidemic model in a time-periodic environment
• Dynamics of a susceptible–infected–susceptible epidemic reaction–diffusion model
• On stationary patterns of a reaction–diffusion model with autocatalysis and saturation law
• Dissipativity and global attractors for a class of quasilinear parabolic systems
• Spatial Ecology via Reaction‐Diffusion Equations
• A priori estimates of stationary solutions of an activator-inhibitor system
• Global Attractors and Steady States for Uniformly Persistent Dynamical Systems

This page was built for publication: Theoretical analysis on a diffusive SIR epidemic model with nonlinear incidence in a heterogeneous environment