ON THE THRESHOLD DYNAMICS OF THE STOCHASTIC SIRS EPIDEMIC MODEL USING ADEQUATE STOPPING TIMES

被引：2
|
作者：
Settati, Adel [1 ]
Lahrouz, Aadil [1 ]
El Jarroudi, Mustapha [1 ]
El Fatini, Mohamed [2 ]
Wang, Kai [3 ]
机构：
[1] Abdelmalek Essaadi Univ, Fac Sci & Tech, Dept Math, Tangier, Morocco
[2] Ibn Tofail Univ, Fac Sci, Dept Math, BP 133, Kenitra, Morocco
[3] Anhui Univ Finance & Econ, Dept Appl Math, Bengbu 233030, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2020年 / 25卷 / 05期
关键词：
Stochastic threshold; SIRS epidemic model; Wiener process; STABILITY; COMPUTATION; EXTINCTION; BEHAVIOR; SYSTEM;
D O I：
10.3934/dcdsb.2020012
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
As it is well known, the dynamics of the stochastic SIRS epidemic model with mass action is governed by a threshold R-S. If R-S < 1 the disease dies out from the population, while if R-S > 1 the disease persists. However, when R-S = 1, classical techniques used to study the asymptotic behaviour do not work any more. In this paper, we give answer to this open problem by using a new approach involving some adequate stopping times. Our results show that if R-S = 1 then, small noises promote extinction while the large one promote persistence. So, it is exactly the opposite role of the noises in case when R-S not equal 1.
引用
收藏
页码：1985 / 1997
页数：13
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