Periodic orbits of a seasonal SIS epidemic model with migration

被引：2

作者：

Sari, Nadir ^{[1
]}

Augeraud-Veron, Emmanuelle ^{[1
]}

机构：

[1] Univ La Rochelle, Lab Math Image & Applicat MIA, F-17042 La Rochelle, France

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 423卷 / 02期

关键词：

Periodic SIS epidemic model; Migrations; Slow-fast system; Averaging; Periodic motion; DISEASE TRANSMISSION; DYNAMICS; THRESHOLD;

D O I：

10.1016/j.jmaa.2014.10.084

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a seasonally forced SIS epidemic model where the population is spatially divided into two patches. We consider that periodicity occurs in the contact rates by switching between two levels. The epidemic dynamics are described by a switched system. We prove the existence of an invariant domain D containing at least one periodic solution. By considering small migrations, we rewrite the SIS model as a slow-fast dynamical system and show that it has a harmonic periodic solution which lies in a small tubular neighborhood of a curve Gamma(m). We deduce from this study the persistence or not of the disease in each patch. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：1849 / 1866

页数：18

共 50 条

[31] The threshold analysis of SIS epidemic model
Guan, Hongjun
Pan, Ju
PROCEEDINGS OF THE 6TH CONFERENCE OF BIOMATHEMATICS, VOLS I AND II: ADVANCES ON BIOMATHEMATICS, 2008, : 191 - 194
[32] ON AN SIS EPIDEMIC MODEL WITH STAGE STRUCTURE
XIAO YanniDepartment of Mathematical Sciences The University of Liverpool Liverpool L ZL UK
Academy of Mathematics and Systems Sciences Academy of Chinese SciencesBeijing ChinaCHEN LansunAcademy of Mathematics and Systems Sciences Academy of Chinese SciencesBeijing China
JournalofSystemsScienceandComplexity, 2003, (02) : 275 - 288
[33] Analysis of an SIS epidemic model with treatment
Wang, Jinghai
Jiang, Qiaohong
ADVANCES IN DIFFERENCE EQUATIONS, 2014, : 1 - 10
[34] A SIS Epidemic Model with Impulsive Vaccination
de la Sen, M.
Alonso-Quesada, S.
Ibeas, A.
2013 IEEE INTERNATIONAL CONFERENCE ON INDUSTRIAL ENGINEERING AND ENGINEERING MANAGEMENT (IEEM 2013), 2013, : 1156 - 1161
[35] An SIS epidemic model with individual variation
Pollett P.K.
Mathematical Biosciences and Engineering, 2024, 21 (04) : 5446 - 5455
[36] ON AN SIS EPIDEMIC MODEL WITH STAGE STRUCTURE
XIAO Yanni(Department of Mathematical Sciences
Academy of Mathematics and Systems Sciences
Journal of Systems Science & Complexity, 2003, (02) : 275 - 288
[37] The SIS epidemic model with Markovian switching
Gray, Alison
Greenhalgh, David
Mao, Xuerong
Pan, Jiafeng
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 394 (02) : 496 - 516
[38] DYNAMICS OF AN IMPROVED SIS EPIDEMIC MODEL
Memarbashi, Reza
Tahavor, Milad
JOURNAL OF THE KOREAN SOCIETY OF MATHEMATICAL EDUCATION SERIES B-PURE AND APPLIED MATHEMATICS, 2023, 30 (02): : 203 - 220
[39] A stochastic SIS epidemic model with vaccination
Cao, Boqiang
Shan, Meijing
Zhang, Qimin
Wang, Weiming
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2017, 486 : 127 - 143
[40] The SIS epidemic model with impulsive effects
Jin, Zhen
Haque, Mainul
SNPD 2007: EIGHTH ACIS INTERNATIONAL CONFERENCE ON SOFTWARE ENGINEERING, ARTIFICIAL INTELLIGENCE, NETWORKING, AND PARALLEL/DISTRIBUTED COMPUTING, VOL 3, PROCEEDINGS, 2007, : 505 - +

← 1 2 3 4 5 →