Analysis of a delayed vaccinated SIR epidemic model with temporary immunity and Levy jumps

被引：90
作者：
Liu, Qun [1 ,2 ]
Jiang, Daqing [1 ,3 ,4 ]
Hayat, Tasawar [3 ,5 ]
Ahmad, Bashir [3 ]
机构：
[1] Northeast Normal Univ, Key Lab Appl Stat MOE, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China
[2] Yulin Normal Univ, Guangxi Coll & Univ Key Lab Complex Syst Optimiza, Sch Math & Stat, Yulin 537000, Guangxi, Peoples R China
[3] King Abdulaziz Univ, Dept Math, Nonlinear Anal & Appl Math NAAM Res Grp, Fac Sci, Jeddah 121589, Saudi Arabia
[4] China Univ Petr East China, Coll Sci, Qingdao 266580, Shandong, Peoples R China
[5] Quaid I Azam Univ, Dept Math, Islamabad 45320, Pakistan
来源：
NONLINEAR ANALYSIS-HYBRID SYSTEMS | 2018年 / 27卷
关键词：
Stochastic delayed SIR epidemic model; Persistence and extinction; Temporary immunity; Vaccination; Levy jumps; STOCHASTIC DIFFERENTIAL-EQUATIONS; NONLINEAR INCIDENCE; GLOBAL STABILITY; INFECTIOUS-DISEASES; THRESHOLD BEHAVIOR; POPULATION BIOLOGY; DYNAMICS; STRATEGY; PERTURBATION; DRIVEN;
D O I：
10.1016/j.nahs.2017.08.002
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we discuss the persistence and extinction of a delayed vaccinated SIR epidemic model with temporary immunity and Levy jumps. Firstly, we study the existence and uniqueness of the global positive solution with any positive initial value. Then we establish sufficient conditions for persistence and extinction of the disease. Moreover, when the noise is large, we find that a large noise intensity has the effect of suppressing the epidemic, so that it goes to extinction. Results show that the persistence and extinction of the disease have a very closed relationship with the intensity of Levy noise and the validity period of the vaccination. Some examples and numerical simulations are carried out to show the effectiveness and feasibility of the theoretical results. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码：29 / 43
页数：15
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