Global stability of a discrete SIR epidemic model with vaccination and treatment

被引：21

作者：

Cui, Qianqian ^{[1
]}

Zhang, Qiang ^{[2
]}

机构：

[1] Nanjing Univ Sci & Technol, Dept Appl Math, Nanjing 210094, Peoples R China

[2] Shihezi Univ, Coll Sci, Shihezi 832000, Xinjiang, Peoples R China

来源：

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2015年 / 21卷 / 02期

关键词：

dynamically consistent; SIR epidemic model; globally asymptotically stable; NSFD scheme; discrete-time model; FINITE-DIFFERENCE SCHEMES; NSFD SCHEME; EQUATIONS;

D O I：

10.1080/10236198.2014.990450

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study a discrete susceptible-infected-removed epidemic model with vaccination and treatment and it is shown that the global dynamics is determined by the basic reproduction number R-0. If R-0 < 1, then the disease-free equilibrium is globally asymptotically stable and if R-0 > 1, then the endemic equilibrium is globally asymptotically stable.

引用

页码：111 / 117

页数：7

共 16 条

[1]

[Anonymous], 2012, P 2 INT C BAS SCI

[2]

[Anonymous], 2000, APPL NONSTANDARD FIN

[3] An NSFD scheme for a class of SIR epidemic models with vaccination and treatment [J].

Cui, Qianqian ;

Yang, Xia ;

Zhang, Qiang .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2014, 20 (03) :416-422

[4] A non-standard finite difference scheme for an epidemic model with vaccination [J].

Ding, Deqiong ;

Ma, Qiang ;

Ding, Xiaohua .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2013, 19 (02) :179-190

[5] Stability analysis in a class of discrete SIRS epidemic models [J].

Hu, Zengyun ;

Teng, Zhidong ;

Jiang, Haijun .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2012, 13 (05) :2017-2033

[6] Complete global stability for an SIR epidemic model with delay - Distributed or discrete [J].

McCluskey, C. Connell .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (01) :55-59

[7] Dynamic consistency: a fundamental principle for constructing nonstandard finite difference schemes for differential equations [J].

Mickens, RE .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2005, 11 (07) :645-653

[8]

Mickens RE, 2005, ADVANCES IN THE APPLICATIONS OF NONSTANDARD FINITE DIFFERENCE SCHEMES, P1, DOI 10.1142/9789812703316

[9]

Mickens RE., 1994, Nonstandard finite difference models of differential equations

[10] Calculation of denominator functions for nonstandard finite difference schemes for differential equations satisfying a positivity condition [J].

Mickens, Ronald E. .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2007, 23 (03) :672-691

← 1 2 →