scholarly journals Correction: Liu, P., et al. Threshold Analysis and Stationary Distribution of a Stochastic Model with Relapse and Temporary Immunity. Symmetry 2020, 12, 331

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 629
Author(s):  
Peng Liu ◽  
Xinzhu Meng ◽  
Haokun Qi
Keyword(s):  
Stochastic Model ◽  
Stationary Distribution ◽  
Threshold Analysis ◽  
Temporary Immunity

The authors wish to make the following corrections and explanations to this paper [...]

scholarly journals Threshold Analysis and Stationary Distribution of a Stochastic Model with Relapse and Temporary Immunity

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 331 ◽  
Author(s):  
Peng Liu ◽  
Xinzhu Meng ◽  
Haokun Qi
Keyword(s):  
Stochastic Model ◽  
Stationary Distribution ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Markov Semigroup ◽  
Threshold Analysis ◽  
Numerical Examples ◽  
Stochastic Properties ◽  
Symmetric Method ◽  
Temporary Immunity

In this paper, a stochastic model with relapse and temporary immunity is formulated. The main purpose of this model is to investigate the stochastic properties. For two incidence rate terms, we apply the ideas of a symmetric method to obtain the results. First, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the extinction and persistence of this system. Then, we investigate the existence of a stationary distribution for this model by employing the theory of an integral Markov semigroup. Finally, the numerical examples are presented to illustrate the analytical findings.

The stationary distribution and ergodicity of a stochastic mutualism model

2018 ◽  
Vol 68 (3) ◽  
pp. 685-690 ◽  
Author(s):  
Jingliang Lv ◽  
Sirun Liu ◽  
Heng Liu
Keyword(s):  
Stochastic Model ◽  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Ergodic Property ◽  
Model Simulations ◽  
Analytical Results ◽  
Stationary Distribution And Ergodicity ◽  
Mutualism Model ◽  
Mutualism System

Abstract This paper is concerned with a stochastic mutualism system with toxicant substances and saturation terms. We obtain the sufficient conditions for the existence of a unique stationary distribution to the equation and it has an ergodic property. It is interesting and surprising that toxicant substances have no effect on the stationary distribution of the stochastic model. Simulations are also carried out to confirm our analytical results.

scholarly journals Stationary distribution and extinction of a stochastic SEIQ epidemic model with a general incidence function and temporary immunity

2021 ◽  
Vol 6 (11) ◽  
pp. 12359-12378
Author(s):  
Yuhuai Zhang ◽  
◽  
Xinsheng Ma ◽  
Anwarud Din ◽  
◽  
...  
Keyword(s):  
Stationary Distribution ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Noise Intensity ◽  
Epidemic Spreading ◽  
General Incidence Rate ◽  
Global Positive Solution ◽  
Simulation Results ◽  
Theoretical Results ◽  
Temporary Immunity

<abstract><p>In this paper, we propose a novel stochastic SEIQ model of a disease with the general incidence rate and temporary immunity. We first investigate the existence and uniqueness of a global positive solution for the model by constructing a suitable Lyapunov function. Then, we discuss the extinction of the SEIQ epidemic model. Furthermore, a stationary distribution for the model is obtained and the ergodic holds by using the method of Khasminskii. Finally, the theoretical results are verified by some numerical simulations. The simulation results show that the noise intensity has a strong influence on the epidemic spreading.</p></abstract>

A MARKOVIAN MODEL FOR COOPERATIVE INTERACTIONS IN PROTEINS

1995 ◽  
Vol 05 (06) ◽  
pp. 835-863 ◽  
Author(s):  
M. ABUNDO ◽  
L. ACCARDI ◽  
N. ROSATO
Keyword(s):  
Stochastic Model ◽  
Chemical Bond ◽  
Stationary Distribution ◽  
Cooperative Behavior ◽  
Critical Value ◽  
Markovian Model ◽  
Birth And Death Processes ◽  
Cooperative Interactions ◽  
The Mean ◽  
Two Parameters

A stochastic model for cooperative interactions in proteins is proposed. The description is based on the theory of Markov’s chains and of birth-and-death processes. Even if the model depends only on two parameters: the mean probability p and the coupling capacity∆p, it presents a surprising wealth of qualitative behaviors when the two parameters are varied. In particular we provide numerical evidence of change of concavity of the stationary distribution at a critical value of the coupling capacity ∆p. The main mathematical feature is that the probability of creating a new chemical bond depends on the total number of bonds already present in the system. In this sense, we speak of a cooperative behavior.

scholarly journals Stationary distribution of a stochastic SIRD epidemic model of Ebola with double saturated incidence rates and vaccination

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Panpan Wang ◽  
Jianwen Jia
Keyword(s):  
Stochastic Model ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Stationary Distribution ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Lyapunov Functions ◽  
Incidence Rates ◽  
Saturated Incidence ◽  
Global Positive Solution

Abstract In this paper, a stochastic SIRD model of Ebola with double saturated incidence rates and vaccination is considered. Firstly, the existence and uniqueness of a global positive solution are obtained. Secondly, by constructing suitable Lyapunov functions and using Khasminskii’s theory, we show that the stochastic model has a unique stationary distribution. Moreover, the extinction of the disease is also analyzed. Finally, numerical simulations are carried out to portray the analytical results.

scholarly journals On the Dynamics Behaviors of a Stochastic Echinococcosis Infection Model with Environmental Noise

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Jianguo Sun ◽  
Huina Zhang ◽  
Daqing Jiang
Keyword(s):  
Stochastic Model ◽  
Stationary Distribution ◽  
Existence And Uniqueness ◽  
Environmental Noise ◽  
Infection Model ◽  
Sufficient Condition ◽  
Main Attention

This paper pays main attention to the dynamics behaviors of a stochastic echinococcosis infection model with environmental noise. The existence and uniqueness of the stochastic model is showed in this paper. We obtain the sufficient condition of the ergodic stationary distribution. What is more, the condition of extinction of the stochastic model is also given.

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