Effect of discretization on dynamical behavior of SEIR and SIR models with nonlinear incidence

被引：41

作者：

Liu, Junli ^{[1
]}

Peng, Baoyang ^{[1
]}

Zhang, Tailei ^{[2
]}

机构：

[1] Xian Polytech Univ, Sch Sci, Xian 710048, Peoples R China

[2] Changian Univ, Sch Sci, Xian 710064, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2015年 / 39卷

基金：

中国国家自然科学基金;

关键词：

Discrete epidemic model; Forward and backward Euler methods; Lyapunov functional; Global stability; Nonlinear incidence; EPIDEMIOLOGIC MODELS; INCIDENCE RATES;

D O I：

10.1016/j.aml.2014.08.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, using the forward Euler and backward Euler methods, we present four discrete epidemic models with the nonlinear incidence rate. We discuss the effect of two discretizations on the stability of the endemic equilibrium for these models. Numerical simulations are performed to illustrate our analytic results. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：60 / 66

页数：7

共 10 条

[1] The existence of codimension-two bifurcation in a discrete SIS epidemic model with standard incidence [J].

Chen, Qiaoling ;

Teng, Zhidong ;

Wang, Lei ;

Jiang, Haijun .

NONLINEAR DYNAMICS, 2013, 71 (1-2) :55-73

[2] A numerical investigation of discrete oscillating epidemic models [J].

D'Innocenzo, A ;

Paladini, F ;

Renna, L .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2006, 364 :497-512

[3] AN EPIDEMIOLOGICAL MODEL WITH A DELAY AND A NONLINEAR INCIDENCE RATE [J].

HETHCOTE, HW ;

LEWIS, MA ;

VANDENDRIESSCHE, P .

JOURNAL OF MATHEMATICAL BIOLOGY, 1989, 27 (01) :49-64

[4]

Hu Z., 2011, J XINJIANG U NATURAL, V28, P446

[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]

Jury E. I., 1964, THEORY APPL Z TRANSF

[7]

Korobeinikov A, 2004, MATH BIOSCI ENG, V1, P57

[8] INFLUENCE OF NONLINEAR INCIDENCE RATES UPON THE BEHAVIOR OF SIRS EPIDEMIOLOGIC MODELS [J].

LIU, WM ;

LEVIN, SA ;

IWASA, Y .

JOURNAL OF MATHEMATICAL BIOLOGY, 1986, 23 (02) :187-204

[9] DYNAMIC BEHAVIOR OF EPIDEMIOLOGIC MODELS WITH NONLINEAR INCIDENCE RATES [J].

LIU, WM ;

HETHCOTE, HW ;

LEVIN, SA .

JOURNAL OF MATHEMATICAL BIOLOGY, 1987, 25 (04) :359-380

[10]

Pan J., 2012, J PREV MED, V46, P343

← 1 →