Global stability and a comparison of SVEIP and delayed SVIP epidemic models with indirect transmission
type: Item
instance of: scholarly article
title: Global stability and a comparison of SVEIP and delayed SVIP epidemic models with indirect transmission
zbMATH Open document ID: 1466.92184
author: Qiang Hou
author: Tao Wang
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 2020-10-07T00:00:00Z
review text: This paper studies global stability of SVEIP and delayed SVIP epidemic models with indirect transmission. The system considered is described as \(\dot{S}=A-S(f(I)+g(P))-\mu S-\nu S+\delta V\), \(\dot{V}=\nu S-\varepsilon V(f(I)+g(P))-\mu V-\delta V\), \(\dot{E}=(S+\varepsilon V)(f(I)+g(P))-(\mu+\sigma)E\), \(\dot{I}=\sigma E-\varphi(I)\) and \(\dot{P}=h(I)-\omega(P)\), where \(S\) is the susceptible compartment, \(V\) is the vaccinated compartment, \(E\) is the exposed compartment, \(I\) is the infectious compartment, and \(P\) is the pathogens in the environment. An infectious animal generates infection with both direct and indirect modes of transmission. The corresponding model with constant time delay has also been considered. Under the assumptions that \(f\), \(g\), \(\varepsilon\), \(h\) and \(\omega\) are sufficiently smooth and some other conditions, the global stability of equilibria are determined by the basic reproduction numbers. If the basic reproduction number is greater than one, it is shown that there exists a unique endemic equilibrium for the systems and it is globally asymptotically stable. Some numerical simulations are presented to illustrate the theoretical results.
reviewed by: Yilun Shang
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 7257302
zbMATH Keywords: delayed system
zbMATH Keywords: basic reproduction number
zbMATH Keywords: global stability
zbMATH Keywords: numerical analysis
MaRDI profile type: Publication
full work available at URL: j.cnsns.2016.07.010
OpenAlex ID: W2464486840
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DOI: 10.1016/J.CNSNS.2016.07.010
description: scientific article; zbMATH DE number 7257302