ON A DELAYED EPIDEMIC MODEL WITH NON-INSTANTANEOUS IMPULSES

被引：30

作者：

Bai, Liang ^{[1
]}

Nieto, Juan J. ^{[2
,3
]}

Uzal, Jose M. ^{[2
,3
]}

机构：

[1] Taiyuan Univ Technol, Coll Math, Taiyuan 030024, Shanxi, Peoples R China

[2] Univ Santiago de Compostela, Fac Matemat, Dept Estat Analise Matemat & Optimizac, Santiago De Compostela 15782, Spain

[3] Univ Santiago de Compostela, Fac Matemat, Inst Matemat, Santiago De Compostela 15782, Spain

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2020年 / 19卷 / 04期

基金：

中国国家自然科学基金;

关键词：

SEIRS epidemic model; pulse vaccination; global attractiveness; permanence; non-instantaneous impulses; DIFFERENTIAL-EQUATIONS; VARIATIONAL APPROACH; VACCINATION; STABILITY;

D O I：

10.3934/cpaa.2020084

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a non-instantaneous pulse vaccination model. Non-instantaneous impulsive nonlinear differential equations provide an adequate biomathematical model of some medical problems. In this paper we study some basic properties such as the attractiveness of the infection-free periodic solution and the permanence of some sub-population for a vaccine model where a constant fraction of the susceptible population is vaccinated in some periodic way. Our model is a system of nonlinear differential equations with impulses.

引用

页码：1915 / 1930

页数：16

共 24 条

[1]

Agarwal R.P., 2017, NONINSTANTANEOUS IMP

[2] Noninstantaneous impulses in Caputo fractional differential equations and practical stability via Lyapunov functions [J].

Agarwal, Ravi ;

Hristova, S. ;

O'Regan, D. .

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2017, 354 (07) :3097-3119

[3]

[Anonymous], 1989, THEORY IMPULSIVE DIF

[4] Variational approach to non-instantaneous impulsive nonlinear differential equations [J].

Bai, Liang ;

Nieto, Juan J. ;

Wang, Xiaoyun .

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2017, 10 (05) :2440-2448

[5] Variational approach to differential equations with not instantaneous impulses [J].

Bai, Liang ;

Nieto, Juan J. .

APPLIED MATHEMATICS LETTERS, 2017, 73 :44-48

[6]

Bainov D., 1993, IMPULSIVE DIFFERENTI, V66

[7] Semilinear fractional differential equations with infinite delay and non-instantaneous impulses [J].

Benchohra, Mouffak ;

Litimein, Sara ;

Nieto, Juan J. .

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2019, 21 (01)

[8]

Brauer F., 2012, MATH MODELS POPULATI, V2, DOI [10.1007/978-1-4614-1686-9, DOI 10.1007/978-1-4614-1686-9]

[9] Analysis of an SEIRS epidemic model with two delays [J].

Cooke, KL ;

vandenDriessche, P .

JOURNAL OF MATHEMATICAL BIOLOGY, 1996, 35 (02) :240-260

[10]

Diekmann O., 2000, Mathematical epidemiology of infectious diseases: Model building, analysis and interpretation, V5

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