ANALYSIS OF A STOCHASTIC RECOVERY-RELAPSE EPIDEMIC MODEL WITH PERIODIC PARAMETERS AND MEDIA COVERAGE

被引：19

作者：

Feng, Tao ^{[1
,2
]}

Qiu, Zhipeng ^{[1
]}

Meng, Xinzhu ^{[2
]}

机构：

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

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

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2019年 / 9卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Stochastic epidemic model; media coverage; periodic solution; vertical transmission; recovery-relapse; NONLINEAR INCIDENCE RATE; DYNAMICS ANALYSIS; VERTICAL TRANSMISSIONS; NUMERICAL SIMULATIONS; INFECTION MODEL; GLOBAL DYNAMICS; DISEASE; SYSTEM;

D O I：

10.11948/2156-907X.20180231

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper addresses, motivated by mathematical work on infectious disease models, the impacts of environmental noise and media coverage on the dynamics of recovery-relapse infectious diseases. A susceptible-infectious-recovered-infectious model is formulated with both vertical transmission and horizontal transmission. The existence and uniqueness of the positive global solution is studied by constructing suitable Lyapunov-type function. Then, the existence of positive periodic solutions is verified by applying Khasminskii's theory. The existence of positive periodic solutions indicates the continued survival of the diseases. Besides, sufficient conditions for the extinction of the diseases are obtained. Numerical simulations then demonstrate the dynamics of the solutions. The paper extends the results of the corresponding deterministic system.

引用

页码：1007 / 1021

页数：15

共 42 条

[1] Periodicity in an epidemic model with a generalized non-linear incidence [J].

Alexander, ME ;

Moghadas, SM .

MATHEMATICAL BIOSCIENCES, 2004, 189 (01) :75-96

[2]

[Anonymous], 2012, STOCHASTIC STABILITY

[3] Refining the Global Spatial Limits of Dengue Virus Transmission by Evidence-Based Consensus [J].

Brady, Oliver J. ;

Gething, Peter W. ;

Bhatt, Samir ;

Messina, Jane P. ;

Brownstein, John S. ;

Hoen, Anne G. ;

Moyes, Catherine L. ;

Farlow, Andrew W. ;

Scott, Thomas W. ;

Hay, Simon I. .

PLOS NEGLECTED TROPICAL DISEASES, 2012, 6 (08)

[4] A stochastic vector-borne epidemic model: Quasi-stationarity and extinction [J].

Britton, Tom ;

Traore, Ali .

MATHEMATICAL BIOSCIENCES, 2017, 289 :89-95

[5] Complex Dynamics of a host parasite model with both horizontal and vertical transmissions in a spatial heterogeneous environment [J].

Cai, Yongli ;

Kang, Yun ;

Banerjee, Malay ;

Wang, Weiming .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2018, 40 :444-465

[6] A new way of investigating the asymptotic behaviour of a stochastic SIS system with multiplicative noise [J].

Chang, Zhengbo ;

Meng, Xinzhu ;

Zhang, Tonghua .

APPLIED MATHEMATICS LETTERS, 2019, 87 :80-86

[7] AN SIS INFECTION MODEL INCORPORATING MEDIA COVERAGE [J].

Cui, Jing-An ;

Tao, Xin ;

Zhu, Huaiping .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2008, 38 (05) :1323-1334

[8] A spatial SIS model in advective heterogeneous environments [J].

Cui, Renhao ;

Lou, Yuan .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 261 (06) :3305-3343

[9] A stochastic model for internal HIV dynamics [J].

Dalal, Nirav ;

Greenhalgh, David ;

Mao, Xuerong .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 341 (02) :1084-1101

[10] GLOBAL ANALYSIS OF A STOCHASTIC TB MODEL WITH VACCINATION AND TREATMENT [J].

Feng, Tao ;

Qiu, Zhipeng .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (06) :2923-2939

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