An SIRS epidemic model with vital dynamics and a ratio-dependent saturation incidence rate
type: Item
instance of: scholarly article
title: An SIRS epidemic model with vital dynamics and a ratio-dependent saturation incidence rate
zbMATH Open document ID: 1418.92199
DOI: 10.1155/2015/720682
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-19T00:00:00Z
review text: Summary: This paper presents an investigation on the dynamics of an epidemic model with vital dynamics and a nonlinear incidence rate of saturated mass action as a function of the ratio of the number of the infectives to that of the susceptibles. The stabilities of the disease-free equilibrium and the endemic equilibrium are first studied. Under the assumption of nonexistence of periodic solution, the global dynamics of the model is established: either the number of infective individuals tends to zero as time evolves or it produces bistability in which there is a region such that the disease will persist if the initial position lies in the region and disappears if the initial position lies outside this region. Computer simulation shows such results.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34C60
zbMATH DE Number: 7025470
Wikidata QID: Q59105391
author: Xin-Li Wang
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/720682
OpenAlex ID: W2190244686
cites work: A generalization of the Kermack-McKendrick deterministic epidemic model
cites work: Dynamical behavior of epidemiological models with nonlinear incidence rates
cites work: Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models
cites work: A disease transmission model in a nonconstant population
cites work: Some epidemiological models with nonlinear 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: 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: Analysis of a Reaction-Diffusion System Modeling Man--Environment--Man Epidemics
cites work: Periodicity in an epidemic model with a generalized non-linear incidence
cites work: Bifurcation Analysis of an SIRS Epidemic Model with Generalized Incidence
cites work: Bifurcations of an epidemic model with non-linear incidence and infection-dependent removal rate
description: scientific article; zbMATH DE number 7025470