Global asymptotic stability for a distributed delay differential-difference system of a Kermack-McKendrick SIR model

We investigate a system of distributed delay differential-difference equations describing an epidemic model of susceptible, infected, recovered and temporary protected population dynamics. A nonlocal term (distributed delay) appears in this model to describe the temporary protection period of the su...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Applicable analysis Ročník 102; číslo 12; s. 3463 - 3475
Hlavní autoři: Adimy, Mostafa, Chekroun, Abdennasser, Kuniya, Toshikazu
Médium: Journal Article
Jazyk:angličtina
Vydáno: Abingdon Taylor & Francis 13.08.2023
Taylor & Francis Ltd
Témata:
Asymptotic properties
Delay
delay differential-difference system
Difference equations
Differential equations
Dynamical Systems
local and global asymptotic stability
Lyapunov-Krasovskii functional
Mathematics
SIR epidemic model
Stability
92D30
34K60
37N25
Lyapunov-Krasovskii functional
Local and global asymptotic stability
Delay differential-difference system
SIR epidemic model
ISSN:0003-6811, 1563-504X
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Abstract We investigate a system of distributed delay differential-difference equations describing an epidemic model of susceptible, infected, recovered and temporary protected population dynamics. A nonlocal term (distributed delay) appears in this model to describe the temporary protection period of the susceptible individuals. We investigate the mathematical properties of the model. We obtain the global asymptotic stability of the two steady states: disease-free and endemic. We construct appropriate Lyapunov functionals where the basic reproduction number appears as a threshold for the global asymptotic behavior of the solution between disease extinction and persistence.
AbstractList We investigate a system of distributed delay differential–difference equations describing an epidemic model of susceptible, infected, recovered and temporary protected population dynamics. A nonlocal term (distributed delay) appears in this model to describe the temporary protection period of the susceptible individuals. We investigate the mathematical properties of the model. We obtain the global asymptotic stability of the two steady states: disease-free and endemic. We construct appropriate Lyapunov functionals where the basic reproduction number appears as a threshold for the global asymptotic behavior of the solution between disease extinction and persistence.
We investigate a system of distributed delay differential-difference equations describing an epidemic model of susceptible, infected, recovered and temporary protected population dynamics. A nonlocal term (distributed delay) appears in this model to describe the temporary protection period of the susceptible individuals. We investigate mathematical properties of the model. We obtain the global asymptotic stability of the two steady states: disease-free and endemic. We construct appropriate Lyapunov functionals where the basic reproduction number appears as a threshold for the global asymptotic behavior of the solution between disease extinction and persistence.
Author Kuniya, Toshikazu
Adimy, Mostafa
Chekroun, Abdennasser
Author_xml – sequence: 1
  givenname: Mostafa
  surname: Adimy
  fullname: Adimy, Mostafa
  organization: Inria
– sequence: 2
  givenname: Abdennasser
  orcidid: 0000-0001-9245-3274
  surname: Chekroun
  fullname: Chekroun, Abdennasser
  email: chekroun@math.univ-lyon1.fr, abdennasser.chekroun@gmail.com
  organization: Université de Tlemcen
– sequence: 3
  givenname: Toshikazu
  surname: Kuniya
  fullname: Kuniya, Toshikazu
  organization: Kobe University
BackLink https://hal.science/hal-03683861$$DView record in HAL
BookMark eNqFkU1rFTEUhoO04G3rTxACrlxMm4_JTC5uLKW2pVcKVcFdOJMPTJuZXJNcZf69GW7rogvdJOTwvC-HPEfoYIqTRegtJaeUSHJGCOGdpPSUEcbq0Qsu2Cu0oqLjjSDt9wO0WphmgV6jo5wfCKFMim6FylWIAwQMeR63JRavcS4w-ODLjF1MGLDxuSQ_7Io12NgAc504Z5OdiofQPD-0xXnOxY44upq6tWkE_dh81rd2MsnrR_zl5h6PsVacoEMHIds3T_cx-vbp8uvFdbO5u7q5ON80upWiNHqgILVbQ0dZTziFXveM9-2wpkKblhgi5DBYZhg42kkmtBYtddQ4rSW3a36M3u97f0BQ2-RHSLOK4NX1-UYts-XfuOzoL1rZd3t2m-LPnc1FPcRdmup6ikkuujXpaV8psad0ijkn6_7WUqIWGepZhlpkqCcZNffhRU77AsXHqSTw4b_pj_u0n6qSEX7HFIwqMIeYXIJJ-6z4vyv-AJWEpMQ
CitedBy_id crossref_primary_10_1007_s12346_024_01093_x
Cites_doi 10.1080/00036811.2018.1551997
10.1007/BF00169563
10.1016/j.automatica.2008.10.024
10.1007/s00285-015-0918-8
10.1007/978-3-319-72122-4
10.3934/mbe.2020067
10.1016/0022-0396(70)90114-2
10.1016/S0362-546X(01)00528-4
10.3934/dcdsb.2015.20.2765
10.3934/mbe.2010.7.837
10.1080/00036811.2016.1139698
10.1007/s11768-010-8178-z
10.1016/j.nonrwa.2012.01.007
10.1016/j.jmaa.2021.125464
10.1007/BF02413530
10.1016/j.jmaa.2009.09.017
10.1007/978-1-4612-4342-7
10.1016/S0362-546X(99)00138-8
10.1016/j.cnsns.2014.07.005
10.1016/j.nonrwa.2008.10.014
ContentType Journal Article
Copyright 2022 Informa UK Limited, trading as Taylor & Francis Group 2022
2022 Informa UK Limited, trading as Taylor & Francis Group
Distributed under a Creative Commons Attribution 4.0 International License
Copyright_xml – notice: 2022 Informa UK Limited, trading as Taylor & Francis Group 2022
– notice: 2022 Informa UK Limited, trading as Taylor & Francis Group
– notice: Distributed under a Creative Commons Attribution 4.0 International License
DBID AAYXX
CITATION
7TB
8FD
FR3
JQ2
KR7
1XC
VOOES
DOI 10.1080/00036811.2022.2075352
DatabaseName CrossRef
Mechanical & Transportation Engineering Abstracts
Technology Research Database
Engineering Research Database
ProQuest Computer Science Collection
Civil Engineering Abstracts
Hyper Article en Ligne (HAL)
Hyper Article en Ligne (HAL) (Open Access)
DatabaseTitle CrossRef
Civil Engineering Abstracts
Engineering Research Database
Technology Research Database
Mechanical & Transportation Engineering Abstracts
ProQuest Computer Science Collection
DatabaseTitleList Civil Engineering Abstracts
DeliveryMethod fulltext_linktorsrc
Discipline Applied Sciences
Mathematics
EISSN 1563-504X
EndPage 3475
ExternalDocumentID oai:HAL:hal-03683861v1
10_1080_00036811_2022_2075352
2075352
Genre Research Article
GroupedDBID --Z
-~X
.7F
.QJ
0BK
0R~
23M
2DF
30N
4.4
5GY
5VS
AAENE
AAGDL
AAHIA
AAJMT
AALDU
AAMIU
AAPUL
AAQRR
ABCCY
ABFIM
ABHAV
ABJNI
ABLIJ
ABPAQ
ABPEM
ABTAI
ABUFD
ABXUL
ABXYU
ACGEJ
ACGFS
ACGOD
ACIWK
ACTIO
ADCVX
ADGTB
ADXPE
AEISY
AENEX
AEOZL
AEPSL
AEYOC
AFKVX
AFRVT
AGDLA
AGMYJ
AHDZW
AIJEM
AIYEW
AJWEG
AKBVH
AKOOK
ALMA_UNASSIGNED_HOLDINGS
ALQZU
AQRUH
AQTUD
AVBZW
AWYRJ
BLEHA
CCCUG
CE4
CS3
DGEBU
DKSSO
EBS
E~A
E~B
F5P
GTTXZ
H13
HF~
HZ~
H~P
IPNFZ
J.P
KYCEM
LJTGL
M4Z
NA5
NY~
O9-
P2P
PQQKQ
RIG
RNANH
ROSJB
RTWRZ
S-T
SNACF
TASJS
TBQAZ
TDBHL
TEJ
TFL
TFT
TFW
TN5
TTHFI
TUROJ
TWF
UPT
UT5
UU3
WH7
ZGOLN
~S~
AAYXX
CITATION
7TB
8FD
FR3
JQ2
KR7
1XC
VOOES
ID FETCH-LOGICAL-c485t-cb1a8cf9a6127031a7c72374b915cd40d058bbe2d2af16825cc541f1dfcc83e93
IEDL.DBID TFW
ISICitedReferencesCount 4
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000795717300001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0003-6811
IngestDate Tue Oct 14 06:53:17 EDT 2025
Wed Aug 13 05:54:11 EDT 2025
Tue Nov 18 22:16:26 EST 2025
Sat Nov 29 05:34:59 EST 2025
Mon Oct 20 23:46:11 EDT 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 12
Keywords 92D30
34K60
37N25
Lyapunov-Krasovskii functional
Local and global asymptotic stability
Delay differential-difference system
SIR epidemic model
Language English
License Distributed under a Creative Commons Attribution 4.0 International License: http://creativecommons.org/licenses/by/4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c485t-cb1a8cf9a6127031a7c72374b915cd40d058bbe2d2af16825cc541f1dfcc83e93
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0001-9245-3274
0000-0003-2732-3830
OpenAccessLink https://hal.science/hal-03683861
PQID 2835690717
PQPubID 53162
PageCount 13
ParticipantIDs hal_primary_oai_HAL_hal_03683861v1
proquest_journals_2835690717
informaworld_taylorfrancis_310_1080_00036811_2022_2075352
crossref_citationtrail_10_1080_00036811_2022_2075352
crossref_primary_10_1080_00036811_2022_2075352
PublicationCentury 2000
PublicationDate 2023-08-13
PublicationDateYYYYMMDD 2023-08-13
PublicationDate_xml – month: 08
  year: 2023
  text: 2023-08-13
  day: 13
PublicationDecade 2020
PublicationPlace Abingdon
PublicationPlace_xml – name: Abingdon
PublicationTitle Applicable analysis
PublicationYear 2023
Publisher Taylor & Francis
Taylor & Francis Ltd
Publisher_xml – name: Taylor & Francis
– name: Taylor & Francis Ltd
References CIT0010
CIT0020
CIT0001
CIT0012
CIT0011
CIT0003
CIT0014
CIT0002
CIT0013
CIT0005
CIT0016
CIT0004
CIT0015
CIT0007
CIT0018
CIT0006
CIT0017
CIT0009
CIT0008
CIT0019
References_xml – ident: CIT0012
  doi: 10.1080/00036811.2018.1551997
– ident: CIT0005
  doi: 10.1007/BF00169563
– ident: CIT0017
  doi: 10.1016/j.automatica.2008.10.024
– ident: CIT0018
  doi: 10.1007/s00285-015-0918-8
– ident: CIT0019
  doi: 10.1007/978-3-319-72122-4
– ident: CIT0001
  doi: 10.3934/mbe.2020067
– ident: CIT0016
  doi: 10.1016/0022-0396(70)90114-2
– ident: CIT0006
  doi: 10.1016/S0362-546X(01)00528-4
– ident: CIT0003
  doi: 10.3934/dcdsb.2015.20.2765
– ident: CIT0009
  doi: 10.3934/mbe.2010.7.837
– ident: CIT0004
  doi: 10.1080/00036811.2016.1139698
– ident: CIT0020
  doi: 10.1007/s11768-010-8178-z
– ident: CIT0011
  doi: 10.1016/j.nonrwa.2012.01.007
– ident: CIT0002
  doi: 10.1016/j.jmaa.2021.125464
– ident: CIT0014
  doi: 10.1007/BF02413530
– ident: CIT0010
  doi: 10.1016/j.jmaa.2009.09.017
– ident: CIT0015
  doi: 10.1007/978-1-4612-4342-7
– ident: CIT0007
  doi: 10.1016/S0362-546X(99)00138-8
– ident: CIT0013
  doi: 10.1016/j.cnsns.2014.07.005
– ident: CIT0008
  doi: 10.1016/j.nonrwa.2008.10.014
SSID ssj0012856
Score 2.3001869
Snippet We investigate a system of distributed delay differential-difference equations describing an epidemic model of susceptible, infected, recovered and temporary...
We investigate a system of distributed delay differential–difference equations describing an epidemic model of susceptible, infected, recovered and temporary...
SourceID hal
proquest
crossref
informaworld
SourceType Open Access Repository
Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 3463
SubjectTerms Asymptotic properties
Delay
delay differential-difference system
Difference equations
Differential equations
Dynamical Systems
local and global asymptotic stability
Lyapunov-Krasovskii functional
Mathematics
SIR epidemic model
Stability
Title Global asymptotic stability for a distributed delay differential-difference system of a Kermack-McKendrick SIR model
URI https://www.tandfonline.com/doi/abs/10.1080/00036811.2022.2075352
https://www.proquest.com/docview/2835690717
https://hal.science/hal-03683861
Volume 102
WOSCitedRecordID wos000795717300001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAWR
  databaseName: Taylor & Francis Online Journals
  customDbUrl:
  eissn: 1563-504X
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0012856
  issn: 0003-6811
  databaseCode: TFW
  dateStart: 19710401
  isFulltext: true
  titleUrlDefault: https://www.tandfonline.com
  providerName: Taylor & Francis
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LS8QwEA66eNCD6xNXVwniNbrpMz0u4qL4QHygt9BOExTX3cVWYf-9mTQtisge9JjQSdtkMplJJt9HyEGUmbCBa2A80jkLIs6ZUBlmWWQ6UhoTMSy6_kV8dSUeH5Nrl01YuLRKjKF1BRRhbTVO7jQr6oy4IwuiIjhGdx7epYoRosRYYePZo47fDR6acwRPWP5WlGAoUt_h-a2Vb6vT_JPNjfyKYPrDYttlaND-hx9YIcvOB6X9SmlWyZwarZG280epm-3FGlm6bDBdi3VSVvQANC2mr5NybCqp8Sxtbu2Umm-nKc0RhRcJtEwziD45pTX_irEjQ1YXQNEKQJqOtZE6x8UBXtglGKufI0w_vT27oZajZ4PcD07ujk-Z42xgEIiwZJDxVIBO0giPtH2exhCb8Q6yhIeQB728F4osU17upZpHJjwFCI2u8FwDCF8l_iZpjcYjtUWoDkDFgCdDOaqTJ0zwFIdhpHXopypOOiSox0qCAzRHXo2h5A3uadXPEvtZun7ukMNGbFIheswS2DeK0DyLeNyn_QuJdfi0LyL-wTsk-aonsrT7LboiR5H-jBd0a6WSzoIUEnHwcOeCx9t_aHqHLJqij5vg3O-SVvn2rnbJAnyUz8Xbnp0rn2m9DVs
linkProvider Taylor & Francis
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LTxsxEB7xqAQ9EBqKGp5W1asB79N7RKhREEkOkKq5WbuztkDQBLFbpPz7erwPpaqqHOC4Xo931zue8djj7wP4FmU2bBAGuYhMzoNICC51RlkWmYm0oUQMh64_jMdjOZ0my2dhKK2SYmhTAUU4W02Dmxajm5S4c4eiIgWFdx4dpooJo2QdNkPraymtb9L_2e4keNIxuJIIJ5nmFM__mvnLP63fu-zIZQzTf2y2c0T9znt8wi7s1NNQdlnpzSdY07MudOopKasHfNGFj6MW1rXYg7JiCGBpsfj1XM5tIbOTS5deu2D25VnKcgLiJQ4t2wwBUC5YQ8FiTckTby5QswpDms2Nlboh_4CPfITW8OeE1M_urm-Zo-n5DD_63ydXA17TNnAMZFhyzEQq0SRpRLvavkhjjO0vD7JEhJgHF_lFKLNMe7mXGhHZCBUxtOoicoMofZ34-7Axm8_0F2AmQB0jbQ7lpFGetPFTHIaRMaGf6jjpQdD8LIU1pjlRazwp0UKfVv2sqJ9V3c89OGvFnitQj1UCX60mtHUJkntwOVRURrV9GYlX0YNkWVFU6ZZcTMWPovwVDzhqtErVRqRQBIVHixciPnhD06ewNZiMhmp4Pb45hG17y6c1ceEfwUb58lsfwwd8LR-KlxM3cP4AXdQRfA
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrZ1LT9wwEIBHhVYIDqXlIbalrVX1aljn6RxR2xWIZYUKVblZydgWVWF3RQLS_vt6HCcCVYgDPcbJOIkzHnvsyTcAX7LKuQ3CIheZ1TzJhODSVBRlUdnMWArE8HT9cT6ZyIuL4jREE9YhrJJ8aNuCIrytps4917aLiNv3EBUpyLuL6F-qnBAlS_DSw7GcSp-PfvUbCZH0CVxJhJNM9xPPY9U8GJ6WLn1w5H2E6T8m249Do_X_8AZv4HWYhLKDVmvewgsz3YD1MCFlobvXG7B20kNd601o2vwArKwX1_Nm5gqZm1r64NoFc8_OSqYJw0sZtFw1hJ9csC4BizMkV7w7QMNagjSbWSd1TKMD_uEn6My-Jk4_Ozv6wXySni34Ofp-_vWQh6QNHBOZNhwrUUq0RZnRnnYsyhxz98GTqhAp6mSoh6msKhPpqLQic_4pYuqURWiLKGNTxNuwPJ1NzQ4wm6DJkbaGNOlTJJ33lKdpZm0alyYvBpB030phIJpTYo0rJXrwadvOitpZhXYewF4vNm-RHk8JfHaK0F9LQO7Dg7GiMro6lpm4EwMo7uuJavyCi22zo6j4iRvsdkqlggmpFYHwaOlC5O-eUfUnWDn9NlLjo8nxe1h1Z2JaEBfxLiw3N7fmA7zCu-Z3ffPRd5u_3nQQIA
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Global+asymptotic+stability+for+a+distributed+delay+differential%E2%80%93difference+system+of+a+Kermack%E2%80%93McKendrick+SIR+model&rft.jtitle=Applicable+analysis&rft.au=Adimy%2C+Mostafa&rft.au=Chekroun%2C+Abdennasser&rft.au=Kuniya%2C+Toshikazu&rft.date=2023-08-13&rft.pub=Taylor+%26+Francis+Ltd&rft.issn=0003-6811&rft.eissn=1563-504X&rft.volume=102&rft.issue=12&rft.spage=3463&rft.epage=3475&rft_id=info:doi/10.1080%2F00036811.2022.2075352&rft.externalDBID=NO_FULL_TEXT
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0003-6811&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0003-6811&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0003-6811&client=summon