A stochastic threshold for an epidemic model with Beddington-DeAngelis incidence, delayed loss of immunity and Levy noise perturbation

被引:24
作者
Berrhazi, Badr-eddine [1 ]
El Fatini, Mohamed [1 ]
Laaribi, Aziz [2 ]
机构
[1] Ibn Tofail Univ, FS, Dept Math, BP 133, Kenitra, Morocco
[2] Hassan II Univ, FS, Dept Math, Casablanca, Morocco
关键词
Stochastic threshold; White noise; Levy noise; DISEASES DRIVEN; STABILITY; DYNAMICS;
D O I
10.1016/j.physa.2018.05.096
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
In this paper we study a stochastic epidemic model with delayed loss of immunity and Levy noise perturbation. We establish the uniqueness of the global positive solution. We also investigate the extinction and the persistence in mean of the disease. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码:312 / 320
页数:9
相关论文
共 24 条
[1]  
ANDERSON R M, 1991
[2]  
Andersson H., 2002, Stochastic Epidemic Models and Their Statistical Analysis
[3]   Stability of epidemic model with time delays influenced by stochastic perturbations [J].
Beretta, E ;
Kolmanovskii, V ;
Shaikhet, L .
MATHEMATICS AND COMPUTERS IN SIMULATION, 1998, 45 (3-4) :269-277
[4]  
Bernoulli D., 1766, MEM MATH PHYS ACAD R
[5]   A stochastic SIRS epidemic model incorporating media coverage and driven by Levy noise [J].
Berrhazi, Badr-eddine ;
El Fatini, Mohamed ;
Laaribi, Aziz ;
Pettersson, Roger ;
Taki, Regragui .
CHAOS SOLITONS & FRACTALS, 2017, 105 :60-68
[6]  
Brauer F., 2008, Mathematical epidemiology, V1945
[7]  
CastilloChavez C, 2002, MATH APPROACHES EM 1
[8]   STABILITY OF STOCHASTIC DELAYED SIR MODEL [J].
Chen, Guoting ;
Li, Tiecheng .
STOCHASTICS AND DYNAMICS, 2009, 9 (02) :231-252
[9]   Stochastic stability and instability of an epidemic model with relapse [J].
El Fatini, Mohamed ;
Lahrouz, Aadil ;
Pettersson, Roger ;
Settati, Adel ;
Taki, Regragui .
APPLIED MATHEMATICS AND COMPUTATION, 2018, 316 :326-341
[10]   A STOCHASTIC DIFFERENTIAL EQUATION SIS EPIDEMIC MODEL [J].
Gray, A. ;
Greenhalgh, D. ;
Hu, L. ;
Mao, X. ;
Pan, J. .
SIAM JOURNAL ON APPLIED MATHEMATICS, 2011, 71 (03) :876-902