Stability analyses of deterministic and stochastic SEIRI epidemic models with nonlinear incidence rates and distributed delay

被引：13

作者：

Zhang, Hong ^{[1
]}

Xia, Juan ^{[1
]}

Georgescu, Paul ^{[2
]}

机构：

[1] Jiangsu Univ, Dept Financial Math, Zhenjiang 212013, Peoples R China

[2] Tech Univ Iasi, Dept Math, Bd Copou 11, Iasi 700506, Romania

来源：

NONLINEAR ANALYSIS-MODELLING AND CONTROL | 2017年 / 22卷 / 01期

基金：

中国国家自然科学基金;

关键词：

compartmental model; delay differential system; nonlinear incidence; disease relapse; global stability of equilibria; Lyapunov functional; DYNAMICS; RELAPSE;

D O I：

10.15388/NA.2017.1.5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, deterministic and stochastic SEIRI epidemic models featuring a distributed latent period and general, unspecified nonlinear incidence and growth rates for the susceptible class are proposed and investigated from a stability viewpoint. By applying Lyapunov-LaSalle invariance principle, we first obtain sufficient conditions for the global stability of equilibria of the deterministic model. On the basis of this result, we subsequently derive sufficient conditions for asymptotic stability of the stochastic model. Finally, numerical simulations are given to illustrate the previously obtained theoretical framework.

引用

页码：64 / 83

页数：20

共 16 条

[1] Modeling seasonal measles transmission in China [J].

Bai, Zhenguo ;

Liu, Dan .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2015, 25 (1-3) :19-26

[2]

BERETTA E, 1995, J MATH BIOL, V33, P250, DOI 10.1007/BF00169563

[3] Predicting and preventing the emergence of antiviral drug resistance in HSV-2 [J].

Blower, SM ;

Porco, TC ;

Darby, G .

NATURE MEDICINE, 1998, 4 (06) :673-678

[4] Analysis of a delayed epidemic model with pulse vaccination and saturation incidence [J].

Gao, Shujing ;

Chen, Lansun ;

Nieto, Juan J. ;

Torres, Angela .

VACCINE, 2006, 24 (35-36) :6037-6045

[5] A Lyapunov functional for a SIRI model with nonlinear incidence of infection and relapse [J].

Georgescu, Paul ;

Zhang, Hong .

APPLIED MATHEMATICS AND COMPUTATION, 2013, 219 (16) :8496-8507

[6] Varicella-zoster virus: Atypical presentations and unusual complications [J].

Gnann, JW .

JOURNAL OF INFECTIOUS DISEASES, 2002, 186 :S91-S98

[7] Positive solutions for a system of second-order nonlinear multi-point eigenvalue problems [J].

Henderson, Johnny ;

Luca, Rodica .

APPLIED MATHEMATICS AND COMPUTATION, 2013, 223 :197-208

[8]

Kuang Y., 1993, Delay Differential Equations with Applications in Population Dynamics

[9] ANALYSIS ON AN EPIDEMIC MODEL WITH A RATIO-DEPENDENT NONLINEAR INCIDENCE RATE [J].

Li, Bo ;

Yuan, Sanling ;

Zhang, Weiguo .

INTERNATIONAL JOURNAL OF BIOMATHEMATICS, 2011, 4 (02) :227-239

[10] Global stability of multi-group epidemic models with distributed delays [J].

Li, Michael Y. ;

Shuai, Zhisheng ;

Wang, Chuncheng .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 361 (01) :38-47

← 1 2 →