Analysis of an SIRS epidemic model with time delay on heterogeneous network

Analysis of an SIRS epidemic model with time delay on heterogeneous network

Abstract We discuss a novel epidemic SIRS model with time delay on a scale-free network in this paper. We give an equation of the basic reproductive number R 0 $R_{0}$ for the model and prove that the disease-free equilibrium is globally attractive and that the disease dies out when R 0 < 1 $R_{0...

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Bibliographic Details
Main Authors: Qiming Liu, Meici Sun, Tao Li
Format: Article
Language:English
Published: SpringerOpen 2017-10-01
Series:Advances in Difference Equations
Subjects:
epidemic spreading
scale-free network
basic reproductive number
global attractiveness
time delay
Online Access:http://link.springer.com/article/10.1186/s13662-017-1367-z
Description
Summary:Abstract We discuss a novel epidemic SIRS model with time delay on a scale-free network in this paper. We give an equation of the basic reproductive number R 0 $R_{0}$ for the model and prove that the disease-free equilibrium is globally attractive and that the disease dies out when R 0 < 1 $R_{0}<1$ , while the disease is uniformly persistent when R 0 > 1 $R_{0}>1$ . In addition, by using a suitable Lyapunov function, we establish a set of sufficient conditions on the global attractiveness of the endemic equilibrium of the system.
ISSN:1687-1847

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