Stochastic dynamics of an SIRS epidemic model with ratio-dependent incidence rate
type: Item
instance of: scholarly article
title: Stochastic dynamics of an SIRS epidemic model with ratio-dependent incidence rate
zbMATH Open document ID: 1302.92123
DOI: 10.1155/2013/172631
author: Yongli Cai
author: Xixi Wang
author: Weiming Wang
author: Min Zhao
published in: Abstract and Applied Analysis
publication date: 2014-06-20T00:00:00Z
review text: Summary: We investigate the complex dynamics of an epidemic model with nonlinear incidence rate of saturated mass action which depends on the ratio of the number of infectious individuals to that of susceptible individuals. We first deal with the boundedness, dissipation, persistence, and the stability of the disease-free and endemic points of the deterministic model. And then we prove the existence and uniqueness of the global positive solutions, stochastic boundedness, and permanence for the stochastic epidemic model. Furthermore, we perform some numerical examples to validate the analytical findings. Needless to say, both deterministic and stochastic epidemic models have their important roles.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34F05
zbMATH DE Number: 6306093
Wikidata QID: Q58915428
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/172631
OpenAlex ID: W1974841834
cites work: Contributions to the mathematical theory of epidemics. II. —The problem of endemicity
cites work: Q3616335
cites work: Non-linear incidence and stability of infectious disease models
cites work: Epidemic threshold conditions for seasonally forced SEIR models
cites work: A generalization of the Kermack-McKendrick deterministic epidemic model
cites work: Q3514986
cites work: Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models
cites work: Dynamical behavior of epidemiological models with nonlinear incidence rates
cites work: Reproduction numbers and thresholds in stochastic epidemic models. I: Homogeneous populations
cites work: A disease transmission model in a nonconstant population
cites work: The mathematics of infectious diseases
cites work: Periodicity in an epidemic model with a generalized non-linear incidence
cites work: Dynamical behavior of an epidemic model with a nonlinear incidence rate
cites work: Global analysis of an epidemic model with nonmonotone incidence rate
cites work: Stability and bifurcation of an SIR epidemic model with nonlinear incidence and treatment
cites work: Global dynamics of an epidemic model with a ratio-dependent nonlinear incidence rate
cites work: Analysis on an epidemic model with a ratio-dependent nonlinear incidence rate
cites work: An Introduction to Stochastic Epidemic Models
cites work: Q3764976
cites work: Stochastic differential equations. An introduction with applications.
cites work: Q4369402
cites work: Long term behavior of solutions of the Lotka-Volterra system under small random perturbations.
cites work: Environmental Brownian noise suppresses explosions in population dynamics.
cites work: Ratio-dependent predator–prey model: effect of environmental fluctuation and stability
cites work: A note on nonautonomous logistic equation with random perturbation
cites work: Stochastic population dynamics under regime switching
cites work: Q3622636
cites work: Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation
cites work: Asymptotic properties of a stochastic predator-prey system with Holling II functional response
cites work: The complex dynamics of a stochastic predator-prey model
cites work: Stability of epidemic model with time delays influenced by stochastic perturbations
cites work: On the stability properties of a stochastic model for phage-bacteria interaction in open marine environment
cites work: Stochastic models of some endemic infections
cites work: A stochastic model of AIDS and condom use
cites work: A stochastic model for internal HIV dynamics
cites work: Global stability of two-group SIR model with random perturbation
cites work: Stochastic epidemic models: a survey
cites work: Analysis of a stochastic SIR epidemic on a random network incorporating household structure
cites work: The long time behavior of DI SIR epidemic model with stochastic perturbation
cites work: Asymptotic behavior of global positive solution to a stochastic SIR model
cites work: A Stochastic Differential Equation SIS Epidemic Model
cites work: Dynamics of positive solutions to SIR and SEIR epidemic models with saturated incidence rates
cites work: Exclusion and persistence in deterministic and stochastic chemostat models
cites work: An algorithmic introduction to numerical simulation of stochastic differential equations
cites work: Q4871212
description: scientific article; zbMATH DE number 6306093