scholarly journals The long time behavior of DI SIR epidemic model with stochastic perturbation

2010 ◽  
Vol 372 (1) ◽  
pp. 162-180 ◽  
Author(s):  
Daqing Jiang ◽  
Chunyan Ji ◽  
Ningzhong Shi ◽  
Jiajia Yu
Keyword(s):  
Epidemic Model ◽  
Stochastic Perturbation ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Long Time

The long-time behavior of a stochastic SIR epidemic model with distributed delay and multidimensional Lévy jumps

2021 ◽  
Author(s):  
Driss Kiouach ◽  
Yassine Sabbar
Keyword(s):  
Epidemic Model ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Time Behavior ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Long Run ◽  
Long Time ◽  
Lévy Jumps

This paper reports novel theoretical and analytical results for a perturbed version of a SIR model with Gamma-distributed delay. Notably, our epidemic model is represented by Itô–Lévy stochastic differential equations in order to simulate sudden and unexpected external phenomena. By using some new and ameliorated mathematical approaches, we study the long-run characteristics of the perturbed delayed model. Within this scope, we give sufficient conditions for two interesting asymptotic properties: extinction and persistence of the epidemic. One of the most interesting results is that the dynamics of the stochastic model are closely related to the intensities of white noises and Lévy jumps, which can give us a good insight into the evolution of the epidemic in some unexpected situations. Our work complements the results of some previous investigations and provides a new approach to predict and analyze the dynamic behavior of epidemics with distributed delay. For illustrative purposes, numerical examples are presented for checking the theoretical study.

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.

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