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Global stability analysis of an SVEIR epidemic model with general incidence rate
In this paper, a susceptible-vaccinated-exposed-infectious-recovered (SVEIR) epidemic model for an infectious disease that spreads in the host population through horizontal transmission is investigated, assuming that the horizontal transmission is governed by an unspecified function [Formula: see te...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer International Publishing
2018
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7149115/ https://www.ncbi.nlm.nih.gov/pubmed/34171003 http://dx.doi.org/10.1186/s13661-018-0961-7 |
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author | Gao, Da-peng Huang, Nan-jing Kang, Shin Min Zhang, Cong |
author_facet | Gao, Da-peng Huang, Nan-jing Kang, Shin Min Zhang, Cong |
author_sort | Gao, Da-peng |
collection | PubMed |
description | In this paper, a susceptible-vaccinated-exposed-infectious-recovered (SVEIR) epidemic model for an infectious disease that spreads in the host population through horizontal transmission is investigated, assuming that the horizontal transmission is governed by an unspecified function [Formula: see text] . The role that temporary immunity (vaccinated-induced) and treatment of infected people play in the spread of disease, is incorporated in the model. The basic reproduction number [Formula: see text] is found, under certain conditions on the incidence rate and treatment function. It is shown that the model exhibits two equilibria, namely, the disease-free equilibrium and the endemic equilibrium. By constructing a suitable Lyapunov function, it is observed that the global asymptotic stability of the disease-free equilibrium depends on [Formula: see text] as well as on the treatment rate. If [Formula: see text] , then the endemic equilibrium is globally asymptotically stable with the help of the Li and Muldowney geometric approach applied to four dimensional systems. Numerical simulations are also presented to illustrate our main results. |
format | Online Article Text |
id | pubmed-7149115 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | Springer International Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-71491152020-04-13 Global stability analysis of an SVEIR epidemic model with general incidence rate Gao, Da-peng Huang, Nan-jing Kang, Shin Min Zhang, Cong Boundary Value Problems Research In this paper, a susceptible-vaccinated-exposed-infectious-recovered (SVEIR) epidemic model for an infectious disease that spreads in the host population through horizontal transmission is investigated, assuming that the horizontal transmission is governed by an unspecified function [Formula: see text] . The role that temporary immunity (vaccinated-induced) and treatment of infected people play in the spread of disease, is incorporated in the model. The basic reproduction number [Formula: see text] is found, under certain conditions on the incidence rate and treatment function. It is shown that the model exhibits two equilibria, namely, the disease-free equilibrium and the endemic equilibrium. By constructing a suitable Lyapunov function, it is observed that the global asymptotic stability of the disease-free equilibrium depends on [Formula: see text] as well as on the treatment rate. If [Formula: see text] , then the endemic equilibrium is globally asymptotically stable with the help of the Li and Muldowney geometric approach applied to four dimensional systems. Numerical simulations are also presented to illustrate our main results. Springer International Publishing 2018-03-27 2018 /pmc/articles/PMC7149115/ /pubmed/34171003 http://dx.doi.org/10.1186/s13661-018-0961-7 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
spellingShingle | Research Gao, Da-peng Huang, Nan-jing Kang, Shin Min Zhang, Cong Global stability analysis of an SVEIR epidemic model with general incidence rate |
title | Global stability analysis of an SVEIR epidemic model with general incidence rate |
title_full | Global stability analysis of an SVEIR epidemic model with general incidence rate |
title_fullStr | Global stability analysis of an SVEIR epidemic model with general incidence rate |
title_full_unstemmed | Global stability analysis of an SVEIR epidemic model with general incidence rate |
title_short | Global stability analysis of an SVEIR epidemic model with general incidence rate |
title_sort | global stability analysis of an sveir epidemic model with general incidence rate |
topic | Research |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7149115/ https://www.ncbi.nlm.nih.gov/pubmed/34171003 http://dx.doi.org/10.1186/s13661-018-0961-7 |
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