Dynamics Analysis of a Nonlinear Stochastic SEIR Epidemic System with Varying Population Size

被引：13

作者：

Han, Xiaofeng ^{[1
]}

Li, Fei ^{[1
]}

Meng, Xinzhu ^{[1
,2
,3
]}

机构：

[1] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China

[2] Shandong Univ Sci & Technol, State Key Lab Min Disaster Prevent & Control Shan, Qingdao 266590, Peoples R China

[3] Shandong Univ Sci & Technol, Minist Sci & Technol, Qingdao 266590, Peoples R China

来源：

ENTROPY | 2018年 / 20卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Stochastic SEIR model; varying population size; vaccination; permanence in mean; stationary distribution; STATIONARY DISTRIBUTION; GLOBAL ANALYSIS; DIFFERENTIAL-EQUATIONS; NUMERICAL SIMULATIONS; MODEL; ERGODICITY; EXTINCTION; THRESHOLD;

D O I：

10.3390/e20050376

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This paper considers a stochastic susceptible exposed infectious recovered (SEIR) epidemic model with varying population size and vaccination. We aim to study the global dynamics of the reduced nonlinear stochastic proportional differential system. We first investigate the existence and uniqueness of global positive solution of the stochastic system. Then the sufficient conditions for the extinction and permanence in mean of the infectious disease are obtained. Furthermore, we prove that the solution of the stochastic system has a unique ergodic stationary distribution under appropriate conditions. Finally, the discussion and numerical simulation are given to demonstrate the obtained results.

引用

页数：20

共 43 条

[1] A stochastic SIRS epidemic model with infectious force under intervention strategies [J].

Cai, Yongli ;

Kang, Yun ;

Banerjee, Malay ;

Wang, Weiming .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (12) :7463-7502

[2] Analysis of a novel stochastic SIRS epidemic model with two different saturated incidence rates [J].

Chang, Zhengbo ;

Meng, Xinzhu ;

Lu, Xiao .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2017, 472 :103-116

[3] Persistence and distribution of a stochastic susceptible-infected-removed epidemic model with varying population size [J].

Chen, Lihong ;

Wei, Fengying .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2017, 483 :386-397

[4] Application of inequalities technique to dynamics analysis of a stochastic eco-epidemiology model [J].

Feng, Tao ;

Meng, Xinzhu ;

Liu, Lidan ;

Gao, Shujing .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016,

[5] 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

[6] Analysis of novel stochastic switched SILI epidemic models with continuous and impulsive control [J].

Gao, Shujing ;

Zhong, Deming ;

Zhang, Yan .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2018, 495 :162-171

[7]

Gard T. C., 1988, INTRO STOCHASTIC DIF

[8] Global Stability for Delay SIR and SEIR Epidemic Models with Nonlinear Incidence Rate [J].

Huang, Gang ;

Takeuchi, Yasuhiro ;

Ma, Wanbiao ;

Wei, Daijun .

BULLETIN OF MATHEMATICAL BIOLOGY, 2010, 72 (05) :1192-1207

[9] Global Hopf bifurcation and permanence of a delayed SEIRS epidemic model [J].

Jiang, Zhichao ;

Ma, Wanbiao ;

Wei, Junjie .

MATHEMATICS AND COMPUTERS IN SIMULATION, 2016, 122 :35-54

[10] Contribution to the mathematical theory of epidemics [J].

Kermack, WO ;

McKendrick, AG .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-CONTAINING PAPERS OF A MATHEMATICAL AND PHYSICAL CHARACTER, 1927, 115 (772) :700-721

← 1 2 3 4 5 →