The Behavior of an SIR Epidemic Model with Stochastic Perturbation

2012 ◽  
Vol 30 (5) ◽  
pp. 755-773 ◽  
Author(s):  
Chunyan Ji ◽  
Daqing Jiang ◽  
Ningzhong Shi
Keyword(s):  
Epidemic Model ◽  
Stochastic Perturbation ◽  
Sir Epidemic Model ◽  
Sir Epidemic

Dynamics of a multigroup SIR epidemic model with stochastic perturbation

Automatica ◽  
2012 ◽  
Vol 48 (1) ◽  
pp. 121-131 ◽  
Author(s):  
Chunyan Ji ◽  
Daqing Jiang ◽  
Qingshan Yang ◽  
Ningzhong Shi
Keyword(s):  
Epidemic Model ◽  
Stochastic Perturbation ◽  
Sir Epidemic Model ◽  
Sir Epidemic

Two-group SIR epidemic model with stochastic perturbation

2012 ◽  
Vol 28 (12) ◽  
pp. 2545-2560 ◽  
Author(s):  
Chun Yan Ji ◽  
Da Qing Jiang ◽  
Ning Zhong Shi
Keyword(s):  
Epidemic Model ◽  
Stochastic Perturbation ◽  
Sir Epidemic Model ◽  
Sir Epidemic

scholarly journals The Behavior of an SVIR Epidemic Model with Stochastic Perturbation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yanan Zhao ◽  
Daqing Jiang
Keyword(s):  
Epidemic Model ◽  
Lyapunov Functions ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Stochastic Perturbation ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Time Average ◽  
The Difference ◽  
Disease Free

We discuss a stochastic SIR epidemic model with vaccination. We investigate the asymptotic behavior according to the perturbation and the reproduction numberR0. We deduce the globally asymptotic stability of the disease-free equilibrium whenR0≤ 1and the perturbation is small, which means that the disease will die out. WhenR0>1, we derive that the disease will prevail, which is measured through the difference between the solution and the endemic equilibrium of the deterministic model in time average. The key to our analysis is choosing appropriate Lyapunov functions.

Analisis Titik Kesetimbangan Dan Kestabilan Penyebaran Penyakit Malaria di Distrik Manokwari Barat Berdasarkan Model Epidemik SIR

2012 ◽  
Vol 8 (2) ◽  
Author(s):  
Fandy Fandy ◽  
Andi Fajeriani Wyrasti ◽  
Tri Widjajanti
Keyword(s):  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Endemic Diseases ◽  
Sir Epidemic

<em>Stability and equilibrium of malaria&rsquo;s epidemics in Manokwari Barat district based on SIR epidemic model will be discussed in this paper. The SIR epidemic model can be applied to make a model of endemic diseases like malaria. Based on this research, there are 2 types of the equilibrium of malaria&rsquo;s epidemics in Manokwari Barat District, endemic and non endemic point.</em>

scholarly journals Global dynamics of a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaodong Wang ◽  
Chunxia Wang ◽  
Kai Wang
Keyword(s):  
Vertical Transmission ◽  
Epidemic Model ◽  
Media Coverage ◽  
Existence And Uniqueness ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Global Dynamics ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Stochastic Sir

AbstractIn this paper, we study a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage. For the deterministic model, we give the basic reproduction number $R_{0}$ R 0 which determines the extinction or prevalence of the disease. In addition, for the stochastic model, we prove existence and uniqueness of the positive solution, and extinction and persistence in mean. Furthermore, we give numerical simulations to verify our results.

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