Stochastic stability and instability of an epidemic model with relapse

被引：42

作者：

El Fatini, Mohamed ^{[1
]}

Lahrouz, Aadil ^{[1
]}

Pettersson, Roger ^{[2
]}

Settati, Adel ^{[3
]}

Taki, Regragui ^{[1
]}

机构：

[1] Ibn Tofail Univ, Dept Math, FS, BP 133, Kenitra, Morocco

[2] Linnaeus Univ, Dept Math, S-35195 Vaxjo, Sweden

[3] FST, LMA, Dept Math, Tanger BP 416, Casablanca, Morocco

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 316卷

关键词：

Stochastic epidemic model; Relapse; Stability; Lyapunov function; GLOBAL STABILITY; NONLINEAR INCIDENCE; DYNAMICS; SIRS; PERSISTENCE; DISEASES; LATENCY; NOISE;

D O I：

10.1016/j.amc.2017.08.037

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a stochastic epidemic model with relapse. First, we prove global positivity of solutions. Then we discuss stability of the disease-free equilibrium state and we show extinction of epidemics using Lyapunov functions. Furthermore we show persistence of the disease under some conditions on parameters of the model. Our numerical simulations confirm the analytical results. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：326 / 341

页数：16

共 28 条

[1]

[Anonymous], 2004, HERPES

[2]

[Anonymous], 2013, Abstraction Appl.

[3]

[Anonymous], 2007, STOCHASTIC DIFFERENT

[4]

[Anonymous], 1982, VIR PERS S

[5]

Arnold L., 1972, STOCHASTIC DIFFERENT

[6] Predicting and preventing the emergence of antiviral drug resistance in HSV-2 [J].

Blower, SM ;

Porco, TC ;

Darby, G .

NATURE MEDICINE, 1998, 4 (06) :673-678

[7] Global stability of an SIR epidemic model with information dependent vaccination [J].

Buonomo, Bruno ;

d'Onofrio, Alberto ;

Lacitignola, Deborah .

MATHEMATICAL BIOSCIENCES, 2008, 216 (01) :9-16

[8] The asymptotic behavior of a stochastic vaccination model with backward bifurcation [J].

Chen, Can ;

Kang, Yanmei .

APPLIED MATHEMATICAL MODELLING, 2016, 40 (11-12) :6051-6068

[9] Dynamics of a Stochastic SIS Epidemic Model with Saturated Incidence [J].

Chen, Can ;

Kang, Yanmei .

ABSTRACT AND APPLIED ANALYSIS, 2014,

[10]

Friedman Avner., 1976, Stochastic differential equations and applications

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