Ergodic stationary distribution of a stochastic SIRS epidemic model incorporating media coverage and saturated incidence rate

2019 ◽  
Vol 514 ◽  
pp. 671-685 ◽  
Author(s):  
Yan Zhang ◽  
Kuangang Fan ◽  
Shujing Gao ◽  
Yingfen Liu ◽  
Shihua Chen
Keyword(s):  
Incidence Rate ◽  
Stationary Distribution ◽  
Epidemic Model ◽  
Media Coverage ◽  
Sirs Epidemic Model ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Stochastic Sirs Epidemic Model

Deterministic and stochastic stability of an SIRS epidemic model with a saturated incidence rate

2017 ◽  
Vol 25 (1) ◽  
Author(s):  
Modeste N’zi ◽  
Jacques Tano
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Deterministic Model ◽  
Random Noise ◽  
Stochastic Version ◽  
Noise Perturbation ◽  
Sirs Epidemic Model ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Disease Free

AbstractIn this paper, we formulate an epidemic model for the spread of an infectious disease in a population of varying size. The total population is divided into three distinct epidemiological subclass of individuals (susceptible, infectious and recovered) and we study a deterministic and stochastic models with saturated incidence rate. The stochastic model is obtained by incorporating a random noise into the deterministic model. In the deterministic case, we briefly discuss the global asymptotic stability of the disease free equilibrium by using a Lyapunov function. For the stochastic version, we study the global existence and positivity of the solution. Under suitable conditions on the intensity of the white noise perturbation, we prove that there are a

scholarly journals Stationary Distribution and Extinction of a Stochastic SIQR Model with Saturated Incidence Rate

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Qiuhua Zhang ◽  
Kai Zhou
Keyword(s):  
Lyapunov Function ◽  
Incidence Rate ◽  
Stationary Distribution ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Sufficient Condition ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Dynamical Properties ◽  
Theoretical Results

In this paper, we consider a stochastic SIQR epidemic model with saturated incidence rate. By constructing a proper Lyapunov function, we obtain the existence and uniqueness of positive solution for this SIQR model. Furthermore, we study the dynamical properties of this stochastic SIQR model; that is, (i) we establish the sufficient condition for the existence of ergodic stationary distribution of the model; (ii) we obtain the extinction of the disease under some conditions. At last, numerical simulations are introduced to illustrate our theoretical results.

Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model with saturated incidence rate

2016 ◽  
Vol 24 (1) ◽  
Author(s):  
Modeste N'zi ◽  
Gérard Kanga
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Global Analysis ◽  
Sirs Epidemic Model ◽  
Saturated Incidence Rate ◽  
Saturated Incidence

AbstractIn this paper, we present an SIRS (Susceptible, Infective, Recovered, Susceptible) epidemic model with a saturated incidence rate and disease causing death in a population of varying size. We define a parameter ℜ

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