A delayed vaccinated epidemic model with nonlinear incidence rate and Lévy jumps

A stochastic susceptible–infectious–recovered epidemic model with nonlinear incidence rate is formulated to discuss the effects of temporary immunity, vaccination, and Le.´vy jumps on the transmission of diseases. We first determine the existence of a unique global positive solution and a positively...

Descripción completa

Detalles Bibliográficos
Autores principales: Fan, Kuangang, Zhang, Yan, Gao, Shujing, Chen, Shihua
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Elsevier B.V. 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7154516/
https://www.ncbi.nlm.nih.gov/pubmed/32308254
http://dx.doi.org/10.1016/j.physa.2019.123379
_version_ 1783521836052512768
author Fan, Kuangang
Zhang, Yan
Gao, Shujing
Chen, Shihua
author_facet Fan, Kuangang
Zhang, Yan
Gao, Shujing
Chen, Shihua
author_sort Fan, Kuangang
collection PubMed
description A stochastic susceptible–infectious–recovered epidemic model with nonlinear incidence rate is formulated to discuss the effects of temporary immunity, vaccination, and Le.´vy jumps on the transmission of diseases. We first determine the existence of a unique global positive solution and a positively invariant set for the stochastic system. Sufficient conditions for extinction and persistence in the mean of the disease are then achieved by constructing suitable Lyapunov functions. Based on the analysis, we conclude that noise intensity and the validity period of vaccination greatly influence the transmission dynamics of the system.
format Online
Article
Text
id pubmed-7154516
institution National Center for Biotechnology Information
language English
publishDate 2020
publisher Elsevier B.V.
record_format MEDLINE/PubMed
spelling pubmed-71545162020-04-14 A delayed vaccinated epidemic model with nonlinear incidence rate and Lévy jumps Fan, Kuangang Zhang, Yan Gao, Shujing Chen, Shihua Physica A Article A stochastic susceptible–infectious–recovered epidemic model with nonlinear incidence rate is formulated to discuss the effects of temporary immunity, vaccination, and Le.´vy jumps on the transmission of diseases. We first determine the existence of a unique global positive solution and a positively invariant set for the stochastic system. Sufficient conditions for extinction and persistence in the mean of the disease are then achieved by constructing suitable Lyapunov functions. Based on the analysis, we conclude that noise intensity and the validity period of vaccination greatly influence the transmission dynamics of the system. Elsevier B.V. 2020-04-15 2019-11-04 /pmc/articles/PMC7154516/ /pubmed/32308254 http://dx.doi.org/10.1016/j.physa.2019.123379 Text en © 2019 Elsevier B.V. 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
Fan, Kuangang
Zhang, Yan
Gao, Shujing
Chen, Shihua
A delayed vaccinated epidemic model with nonlinear incidence rate and Lévy jumps
title A delayed vaccinated epidemic model with nonlinear incidence rate and Lévy jumps
title_full A delayed vaccinated epidemic model with nonlinear incidence rate and Lévy jumps
title_fullStr A delayed vaccinated epidemic model with nonlinear incidence rate and Lévy jumps
title_full_unstemmed A delayed vaccinated epidemic model with nonlinear incidence rate and Lévy jumps
title_short A delayed vaccinated epidemic model with nonlinear incidence rate and Lévy jumps
title_sort delayed vaccinated epidemic model with nonlinear incidence rate and lévy jumps
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7154516/
https://www.ncbi.nlm.nih.gov/pubmed/32308254
http://dx.doi.org/10.1016/j.physa.2019.123379
work_keys_str_mv AT fankuangang adelayedvaccinatedepidemicmodelwithnonlinearincidencerateandlevyjumps
AT zhangyan adelayedvaccinatedepidemicmodelwithnonlinearincidencerateandlevyjumps
AT gaoshujing adelayedvaccinatedepidemicmodelwithnonlinearincidencerateandlevyjumps
AT chenshihua adelayedvaccinatedepidemicmodelwithnonlinearincidencerateandlevyjumps
AT fankuangang delayedvaccinatedepidemicmodelwithnonlinearincidencerateandlevyjumps
AT zhangyan delayedvaccinatedepidemicmodelwithnonlinearincidencerateandlevyjumps
AT gaoshujing delayedvaccinatedepidemicmodelwithnonlinearincidencerateandlevyjumps
AT chenshihua delayedvaccinatedepidemicmodelwithnonlinearincidencerateandlevyjumps

Ejemplares similares