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Global dynamics for a Filippov epidemic system with imperfect vaccination
Given imperfect vaccination we extend the existing non-smooth models by considering susceptible and vaccinated individuals enhance the protection and control strategies once the number of infected individuals exceeds a certain level. On the basis of global dynamics of two subsystems, for the formula...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Elsevier Ltd.
2020
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7339777/ http://dx.doi.org/10.1016/j.nahs.2020.100932 |
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author | Zhang, Yunhu Xiao, Yanni |
author_facet | Zhang, Yunhu Xiao, Yanni |
author_sort | Zhang, Yunhu |
collection | PubMed |
description | Given imperfect vaccination we extend the existing non-smooth models by considering susceptible and vaccinated individuals enhance the protection and control strategies once the number of infected individuals exceeds a certain level. On the basis of global dynamics of two subsystems, for the formulated Filippov system, we examine the sliding mode dynamics, the boundary equilibrium bifurcations, and the global dynamics. Our main results show that it is possible that the pseudo-equilibrium exists and is globally stable, or the pseudo-equilibrium, the disease-free equilibrium and the real equilibrium are tri-stable, or the pseudo-equilibrium and the real equilibrium are bi-stable, or the pseudo-equilibrium and disease-free equilibrium are bi-stable, which depend on the threshold value and other parameter values. The global stability of the disease-free equilibrium or pseudo-equilibrium reveals that we may eradicate the disease or maintain the number of infected individuals at a previously given value. Further, the bi-stability and tri-stability imply that whether the number of infected individuals tends to zero or a previously given value or other positive values depends on the parameter values and the initial states of the system. This emphasizes the importance of threshold policy and challenges in the control of infectious diseases if without perfect vaccines. |
format | Online Article Text |
id | pubmed-7339777 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | Elsevier Ltd. |
record_format | MEDLINE/PubMed |
spelling | pubmed-73397772020-07-07 Global dynamics for a Filippov epidemic system with imperfect vaccination Zhang, Yunhu Xiao, Yanni Nonlinear Analysis: Hybrid Systems Article Given imperfect vaccination we extend the existing non-smooth models by considering susceptible and vaccinated individuals enhance the protection and control strategies once the number of infected individuals exceeds a certain level. On the basis of global dynamics of two subsystems, for the formulated Filippov system, we examine the sliding mode dynamics, the boundary equilibrium bifurcations, and the global dynamics. Our main results show that it is possible that the pseudo-equilibrium exists and is globally stable, or the pseudo-equilibrium, the disease-free equilibrium and the real equilibrium are tri-stable, or the pseudo-equilibrium and the real equilibrium are bi-stable, or the pseudo-equilibrium and disease-free equilibrium are bi-stable, which depend on the threshold value and other parameter values. The global stability of the disease-free equilibrium or pseudo-equilibrium reveals that we may eradicate the disease or maintain the number of infected individuals at a previously given value. Further, the bi-stability and tri-stability imply that whether the number of infected individuals tends to zero or a previously given value or other positive values depends on the parameter values and the initial states of the system. This emphasizes the importance of threshold policy and challenges in the control of infectious diseases if without perfect vaccines. Elsevier Ltd. 2020-11 2020-06-15 /pmc/articles/PMC7339777/ http://dx.doi.org/10.1016/j.nahs.2020.100932 Text en © 2020 Elsevier Ltd. All rights reserved. Since January 2020 Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre - including this research content - immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active. |
spellingShingle | Article Zhang, Yunhu Xiao, Yanni Global dynamics for a Filippov epidemic system with imperfect vaccination |
title | Global dynamics for a Filippov epidemic system with imperfect vaccination |
title_full | Global dynamics for a Filippov epidemic system with imperfect vaccination |
title_fullStr | Global dynamics for a Filippov epidemic system with imperfect vaccination |
title_full_unstemmed | Global dynamics for a Filippov epidemic system with imperfect vaccination |
title_short | Global dynamics for a Filippov epidemic system with imperfect vaccination |
title_sort | global dynamics for a filippov epidemic system with imperfect vaccination |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7339777/ http://dx.doi.org/10.1016/j.nahs.2020.100932 |
work_keys_str_mv | AT zhangyunhu globaldynamicsforafilippovepidemicsystemwithimperfectvaccination AT xiaoyanni globaldynamicsforafilippovepidemicsystemwithimperfectvaccination |