Stationary distribution and threshold dynamics of a stochastic SIRS model with a general incidence

被引：22
|
作者：
El Fatini, Mohamed [1 ]
El Khalifi, Mohamed [1 ]
Gerlach, Richard [2 ]
Laaribi, Aziz [3 ]
Taki, Regragui [4 ]
机构：
[1] Ibn Tofail Univ, Fac Sci, Dept Math, BP 133, Kenitra, Morocco
[2] Univ Sydney, Business Sch, Discipline Business Analyt, Sydney, NSW, Australia
[3] Sultan Moulay Slimane Univ, Polydisciplinary Fac, Beni Mellal, Morocco
[4] Chouaib Doukkali Univ, High Sch Technol Sidi Bennour, El Jadida, Morocco
来源：
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2019年 / 534卷
关键词：
Epidemic model; Extinction; Persistence; Stationary distribution; LONG-TIME BEHAVIOR; EPIDEMIC MODEL; NONLINEAR INCIDENCE; GLOBAL DYNAMICS; STABILITY;
D O I：
10.1016/j.physa.2019.03.061
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper, we consider a stochastic epidemic model with relapse, cure and a nonlinear incidence rate function. Firstly, we show the existence and uniqueness of a global positive solution. Then, in terms of a stochastic threshold R-s(0). we prove the extinction of the disease when R-s(0) < 1. We also establish the persistence in mean of the epidemic in the case of R-s(0) > 1. Furthermore, we prove the existence of a stationary distribution and its asymptotic stability. Finally, we present numerical simulations for the stochastic model to support the theoretical results. (C) 2019 Elsevier B.V. All rights reserved.
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页数：14
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