Analysis of a stochastic distributed delay epidemic model with relapse and Gamma distribution kernel

被引：44
作者：
Caraballo, Tomas [1 ]
El Fatini, Mohamed [2 ]
El Khalifi, Mohamed [2 ]
Gerlach, Richard [3 ]
Pettersson, Roger [4 ]
机构：
[1] Univ Seville, Dept Ecuac Diferenciales & Anal Numer, Fac Matemat, Tarfia S-N, E-41012 Seville, Spain
[2] Ibn Tofail Univ, Fac Sci, Dept Math, Kenitra BP 133, Kenitra, Morocco
[3] Univ Sydney, Business Sch, Discipline Business Analyt, Sydney, NSW, Australia
[4] Linnaeus Univ, Dept Math, S-35195 Vaxjo, Sweden
来源：
CHAOS SOLITONS & FRACTALS | 2020年 / 133卷
关键词：
Epidemic model; Distributed delay; Extinction; Persistence; Stationary distribution; MATHEMATICAL-THEORY; GLOBAL STABILITY; SIR MODEL; DYNAMICS; THRESHOLD;
D O I：
10.1016/j.chaos.2020.109643
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this work, we investigate a stochastic epidemic model with relapse and distributed delay. First, we prove that our model possesses and unique global positive solution. Next, by means of the Lyapunov method, we determine some sufficient criteria for the extinction of the disease and its persistence. In addition, we establish the existence of a unique stationary distribution to our model. Finally, we provide some numerical simulations for the stochastic model to assist and show the applicability and efficiency of our results. (C) 2020 Elsevier Ltd. All rights reserved.
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页数：8
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