DYNAMICS OF A STOCHASTIC SIR MODEL WITH BOTH HORIZONTAL AND VERTICAL TRANSMISSION

被引：40

作者：

Miao, Anqi ^{[1
]}

Zhang, Tongqian ^{[1
,2
]}

Zhang, Jian ^{[1
]}

Wang, Chaoyang ^{[1
]}

机构：

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

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

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2018年 / 8卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Stochastic SIR epidemic model; vertical transmission; extinction; persistence; threshold; EPIDEMIC MODEL; PULSE VACCINATION; BEHAVIOR; STABILITY; INFECTION; SYSTEM;

D O I：

10.11948/2018.1108

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A stochastic mathematical model with both horizontal and vertical transmission is proposed to investigate the dynamical behavior of SIR disease. By employing theories of stochastic differential equation and inequality techniques, the threshold associating on extinction and persistence of infectious diseases is deduced for the case of the small noise. Our results show that the threshold completely depends on the stochastic perturbation and the basic reproductive number of the corresponding deterministic model. Moreover, we find that large noise is conducive to control the spread of diseases and the persistent disease in deterministic model may eliminate ultimately due to the effect of large noise. Finally, numerical simulations are performed to illustrate the theoretical results.

引用

页码：1108 / 1121

页数：14

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