Dynamical behavior of a new epidemiological model
type: Item
instance of: scholarly article
title: Dynamical behavior of a new epidemiological model
zbMATH Open document ID: 1406.92634
DOI: 10.1155/2014/854528
author: Zizi Wang
author: Zhiming Guo
published in: Journal of Applied Mathematics
publication date: 2019-02-01T00:00:00Z
review text: Summary: A new epidemiological model is introduced with nonlinear incidence, in which the infected disease may lose infectiousness and then evolves to a chronic noninfectious disease when the infected disease has not been cured for a certain time \(\tau\). The existence, uniqueness, and stability of the disease-free equilibrium and endemic equilibrium are discussed. The basic reproductive number \(R_0\) is given. The model is studied in two cases: with and without time delay. For the model without time delay, the disease-free equilibrium is globally asymptotically stable provided that \(R_0\leq 1\); if \(R_0> 1\), then there exists a unique endemic equilibrium, and it is globally asymptotically stable. For the model with time delay, a sufficient condition is given to ensure that the disease-free equilibrium is locally asymptotically stable. Hopf bifurcation in endemic equilibrium with respect to the time \(\tau\) is also addressed.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 92C60
zbMATH DE Number: 7010778
Wikidata QID: Q58005288
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/854528
OpenAlex ID: W1978003634
DBLP publication ID: journals/jam/WangG14
description: scientific article; zbMATH DE number 7010778