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Global threshold dynamics of a stochastic differential equation SIS model
详细信息
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作者:
Chuang Xu
cx1@ualberta.ca" class="auth_mail" title="E-mail the corresponding author
关键词:
SIS epidemic model
;
Global threshold dynamics
;
Basic reproduction number
;
Invariant density
;
Stochastic differential equation
;
Fokker&ndash
;
Planck equation
刊名:Journal of Mathematical Analysis and Applications
出版年:2017
出版时间:15 March 2017
年:2017
卷:447
期:2
页码:736-757
全文大小:799 K
文摘
In this paper, we further investigate the global dynamics of a stochastic differential equation SIS (Susceptible–Infected–Susceptible) epidemic model recently proposed in Gray et al. (2011)
[8]
. We present a stochastic threshold theorem in term of a
stochastic basic reproduction number
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: the disease dies out with probability one if
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, and the disease is recurrent if
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. We prove the existence and global asymptotic stability of a unique invariant density for the Fokker–Planck equation associated with the SDE SIS model when
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. In term of the profile of the invariant density, we define a
persistence basic reproduction number
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and give a persistence threshold theorem: the disease dies out with large probability if
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⩽
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, while persists with large probability if
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>
1
. Comparing the
stochastic disease prevalence
with the
deterministic disease prevalence
, we discover that the stochastic prevalence is bigger than the deterministic prevalence if the deterministic basic reproduction number
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R
0
D
>
2
. This shows that noise may increase severity of disease. Finally, we study the asymptotic dynamics of the stochastic SIS model as the noise vanishes and establish a sharp connection with the threshold dynamics of the deterministic SIS model in term of a
Limit Stochastic Threshold Theorem
.
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