Stationary distribution and extinction of a multi-stage HIV model with nonlinear stochastic perturbation

2021 ◽  
Author(s):  
Chun Lu ◽  
Guanzhen Sun ◽  
Yanmin Zhang
Keyword(s):  
Stationary Distribution ◽  
Stochastic Perturbation ◽  
Hiv Model ◽  
Multi Stage

scholarly journals Existence, Stationary Distribution, and Extinction of Predator-Prey System of Prey Dispersal with Stochastic Perturbation

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Li Zu ◽  
Daqing Jiang ◽  
Fuquan Jiang
Keyword(s):  
Numerical Simulation ◽  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Ergodic Property ◽  
Unique Positive Solution ◽  
Initial Value ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System

We consider a predator-prey model in which the preys disperse amongnpatches (n≥2) with stochastic perturbation. We show that there is a unique positive solution and find out the sufficient conditions for the extinction to the system with any given positive initial value. In addition, we investigate that there exists a stationary distribution for the system and it has ergodic property. Finally, we illustrate the dynamic behavior of the system withn=2via numerical simulation.

scholarly journals Existence, Uniqueness and Ergodicity of Positive Solution of Mutualism System with Stochastic Perturbation

2010 ◽  
Vol 2010 ◽  
pp. 1-18 ◽  
Author(s):  
Chunyan Ji ◽  
Daqing Jiang ◽  
Hong Liu ◽  
Qingshan Yang
Keyword(s):  
Positive Solution ◽  
Stationary Distribution ◽  
Nonnegative Solution ◽  
Stochastic Perturbation ◽  
Ergodic Property ◽  
Mutualism System

We discuss a two-species Lotka-Volterra mutualism system with stochastic perturbation. We show that there is a unique nonnegative solution of this system. Furthermore, we investigate that there exists a stationary distribution for this system, and it has ergodic property.

GLOBAL STABILITY OF AN HIV/AIDS MODEL WITH STOCHASTIC PERTURBATION

2011 ◽  
Vol 04 (02) ◽  
pp. 349-358 ◽  
Author(s):  
Junyuan Yang ◽  
Xiaoyan Wang ◽  
Xuezhi Li
Keyword(s):  
Stochastic Perturbation ◽  
Endemic Equilibrium ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Asymptotically Stable ◽  
Ode Model ◽  
Globally Asymptotically Stable ◽  
Stochastic Perturbations ◽  
Hiv Model ◽  
Disease Free

In this paper, we investigate the dynamic behavior of an HIV model with stochastic perturbation. Firstly, in ODE model, the disease-free equilibrium E0 is globally asymptotically stable if the basic reproductive number R0 < 1. When R0 > 1, the endemic equilibrium E* is globally asymptotically stable. Secondly, the criterion for robustness of the system is established under stochastic perturbations. The conditions of stochastic stability of the endemic equilibrium E* are obtained. Finally, we simulate our analytical results.

scholarly journals Extinction and Stationary Distribution of a Stochastic SIRS Epidemic Model Incorporating Media Coverage

2019 ◽  
pp. 1-19
Author(s):  
Eric N'zi ◽  
Modeste N'zi
Keyword(s):  
Numerical Simulations ◽  
Stationary Distribution ◽  
Epidemic Model ◽  
Media Coverage ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Demographic Stochasticity ◽  
Sirs Epidemic Model ◽  
The Media ◽  
Well Posed

In this paper, we include stochastic perturbation into SIRS epidemic model incorporating media coverage and study their dynamics. Our model is obtained by taking into account both for demographic stochasticity and environmental fluctuations on contact rate before alert media β1. First, we show that the model is biologically well-posed by proving the global existence, positivity and boundedness of solution . Then, sufficient conditions for the extinction of infectious diseaseis proved. We also established sufficient conditions for the existence of an ergodic stationary distribution to the model. Finally, the theoretical results are illustrated by numerical simulations; in addition we show that the media coverage can reduce the peak of infective individuals via numerical simulations.

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