Stationary distribution of a chemostat model with distributed delay and stochastic perturbations

2021 ◽  
pp. 107585
Author(s):  
Miaomiao Gao ◽  
Daqing Jiang
Keyword(s):  
Stationary Distribution ◽  
Distributed Delay ◽  
Chemostat Model ◽  
Stochastic Perturbations

scholarly journals A Stochastic SIR Epidemic System with a Nonlinear Relapse

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Ali El Myr ◽  
Abdelaziz Assadouq ◽  
Lahcen Omari ◽  
Adel Settati ◽  
Aadil Lahrouz
Keyword(s):  
Numerical Simulations ◽  
Stationary Distribution ◽  
Stochastic Perturbations ◽  
Sir Epidemic ◽  
Spread Model ◽  
Stochastic Sir ◽  
Theoretical Results

We investigate the conditions that control the extinction and the existence of a unique stationary distribution of a nonlinear mathematical spread model with stochastic perturbations in a population of varying size with relapse. Numerical simulations are carried out to illustrate the theoretical results.

The asymptotic behavior of a stochastic multigroup SIS model

2018 ◽  
Vol 11 (03) ◽  
pp. 1850037 ◽  
Author(s):  
Chunyan Ji ◽  
Daqing Jiang
Keyword(s):  
Asymptotic Behavior ◽  
Numerical Simulations ◽  
Stationary Distribution ◽  
Endemic Equilibrium ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Sis Model ◽  
Stochastic Perturbations ◽  
Long Time ◽  
Theoretical Results

In this paper, we explore the long time behavior of a multigroup Susceptible–Infected–Susceptible (SIS) model with stochastic perturbations. The conditions for the disease to die out are obtained. Besides, we also show that the disease is fluctuating around the endemic equilibrium under some conditions. Moreover, there is a stationary distribution under stronger conditions. At last, some numerical simulations are applied to support our theoretical results.

scholarly journals Deterministic and Stochastic Study for an Infected Computer Network Model Powered by a System of Antivirus Programs

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Youness El Ansari ◽  
Ali El Myr ◽  
Lahcen Omari
Keyword(s):  
Equilibrium State ◽  
Stationary Distribution ◽  
Computer Network ◽  
Reproduction Number ◽  
Sufficient Condition ◽  
Stochastic Perturbations ◽  
Stochastic Fluctuations ◽  
Spread Model ◽  
The Stability ◽  
Theoretical Results

We investigate the various conditions that control the extinction and stability of a nonlinear mathematical spread model with stochastic perturbations. This model describes the spread of viruses into an infected computer network which is powered by a system of antivirus software. The system is analyzed by using the stability theory of stochastic differential equations and the computer simulations. First, we study the global stability of the virus-free equilibrium state and the virus-epidemic equilibrium state. Furthermore, we use the Itô formula and some other theoretical theorems of stochastic differential equation to discuss the extinction and the stationary distribution of our system. The analysis gives a sufficient condition for the infection to be extinct (i.e., the number of viruses tends exponentially to zero). The ergodicity of the solution and the stationary distribution can be obtained if the basic reproduction number Rp is bigger than 1, and the intensities of stochastic fluctuations are small enough. Numerical simulations are carried out to illustrate the theoretical results.

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