Modeling a stochastic avian influenza model under regime switching and with human-to-human transmission

2020 ◽  
Vol 13 (07) ◽  
pp. 2050064
Author(s):  
Zhenfeng Shi ◽  
Xinhong Zhang
Keyword(s):  
Avian Influenza ◽  
Numerical Simulations ◽  
Stationary Distribution ◽  
Stochastic System ◽  
Regime Switching ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Analytical Results

In this paper, we investigate the stochastic avian influenza model with human-to-human transmission, which is disturbed by both white and telegraph noises. First, we show that the solution of the stochastic system is positive and global. Furthermore, by using stochastic Lyapunov functions, we establish sufficient conditions for the existence of a unique ergodic stationary distribution. Then we obtain the conditions for extinction. Finally, numerical simulations are employed to demonstrate the analytical results.

scholarly journals Dynamic Analysis of a Stochastic Rumor Propagation Model with Regime Switching

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3277
Author(s):  
Fangju Jia ◽  
Chunzheng Cao
Keyword(s):  
Dynamic Analysis ◽  
Numerical Simulations ◽  
Stationary Distribution ◽  
Regime Switching ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Propagation Model ◽  
Rumor Propagation ◽  
White Noises

We study the rumor propagation model with regime switching considering both colored and white noises. Firstly, by constructing suitable Lyapunov functions, the sufficient conditions for ergodic stationary distribution and extinction are obtained. Then we obtain the threshold Rs which guarantees the extinction and the existence of the stationary distribution of the rumor. Finally, numerical simulations are performed to verify our model. The results indicated that there is a unique ergodic stationary distribution when Rs>1. The rumor becomes extinct exponentially with probability one when Rs<1.

scholarly journals Dynamics of a stochastic HIV/AIDS model with treatment under regime switching

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Miaomiao Gao ◽  
Daqing Jiang ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Stationary Distribution ◽  
Regime Switching ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Aids Model ◽  
Telegraph Noise ◽  
Spread Dynamics ◽  
Global Positive Solution ◽  
Theoretical Results ◽  
Hiv Aids

<p style='text-indent:20px;'>This paper focuses on the spread dynamics of an HIV/AIDS model with multiple stages of infection and treatment, which is disturbed by both white noise and telegraph noise. Switching between different environmental states is governed by Markov chain. Firstly, we prove the existence and uniqueness of the global positive solution. Then we investigate the existence of a unique ergodic stationary distribution by constructing suitable Lyapunov functions with regime switching. Furthermore, sufficient conditions for extinction of the disease are derived. The conditions presented for the existence of stationary distribution improve and generalize the previous results. Finally, numerical examples are given to illustrate our theoretical results.</p>

scholarly journals Stationary Distribution and Dynamic Behaviour of a Stochastic SIVR Epidemic Model with Imperfect Vaccine

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Driss Kiouach ◽  
Lahcen Boulaasair
Keyword(s):  
Numerical Simulations ◽  
Stationary Distribution ◽  
Epidemic Model ◽  
Critical Condition ◽  
Dynamic Behaviour ◽  
Sufficient Conditions ◽  
Analytical Results ◽  
The Mean

We consider a stochastic SIVR (susceptible-infected-vaccinated-recovered) epidemic model with imperfect vaccine. First, we obtain critical condition under which the disease is persistent in the mean. Second, we establish sufficient conditions for the existence of an ergodic stationary distribution to the model. Third, we study the extinction of the disease. Finally, numerical simulations are given to support the analytical results.

scholarly journals The Dynamics of a Stochastic SEITRmodel for Tuberculosis with Incomplete Treatment

2021 ◽  
Author(s):  
Xiaodong Wang ◽  
Chunxia Wang ◽  
k wang
Keyword(s):  
Numerical Simulations ◽  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Numerical Results ◽  
Transmission Dynamics ◽  
Environmental Perturbations ◽  
Analytical Results

Abstract In this paper, a stochastic SEITR model is formulated to describe the transmission dynamics of tuberculosis with incompletely treated. Sufficient conditions for the existence of a stationary distribution and extinction are obtained. In addition, numerical simulations are given to illustrate these analytical results. Theoretical and numerical results show that large environmental perturbations can inhibit the spread of tuberculosis.

Dynamics of a stochastic heroin epidemic model with bilinear incidence and varying population size

2019 ◽  
Vol 12 (01) ◽  
pp. 1950005 ◽  
Author(s):  
Shitao Liu ◽  
Liang Zhang ◽  
Xiao-Bing Zhang ◽  
Aibing Li
Keyword(s):  
Numerical Simulations ◽  
Population Size ◽  
Stationary Distribution ◽  
Epidemic Model ◽  
Lyapunov Functions ◽  
Drug Abusers ◽  
Analytical Results ◽  
Varying Population ◽  
Better Than

We investigate a stochastic heroin epidemic model with bilinear incidence and varying population size. Sufficient criteria for the extinction of the drug abusers and the existence of ergodic stationary distribution for the model are established by constructing suitable stochastic Lyapunov functions. By analyzing the sensitivity of the threshold of spread, we obtain that prevention is better than cure. Numerical simulations are carried out to confirm the analytical results.

Stationary distribution and periodic solution of stochastic chemostat models with single-species growth on two nutrients

2019 ◽  
Vol 12 (06) ◽  
pp. 1950063 ◽  
Author(s):  
Miaomiao Gao ◽  
Daqing Jiang ◽  
Tasawar Hayat
Keyword(s):  
Periodic Solution ◽  
Numerical Simulations ◽  
Stationary Distribution ◽  
Markov Processes ◽  
Lyapunov Functions ◽  
Autonomous System ◽  
Random Perturbation ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Single Species

In this paper, we consider two chemostat models with random perturbation, in which single species depends on two perfectly substitutable resources for growth. For the autonomous system, we first prove that the solution of the system is positive and global. Then we establish sufficient conditions for the existence of an ergodic stationary distribution by constructing appropriate Lyapunov functions. For the non-autonomous system, by using Has’minskii theory on periodic Markov processes, we derive it admits a nontrivial positive periodic solution. Finally, numerical simulations are carried out to illustrate our main results.

scholarly journals Asymptotic Behavior Analysis for a Three-Species Food Chain Stochastic Model with Regime Switching

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Junmei Liu ◽  
Yonggang Ma
Keyword(s):  
Asymptotic Behavior ◽  
Lyapunov Function ◽  
Stochastic Model ◽  
Numerical Simulations ◽  
Behavior Analysis ◽  
Food Chain ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
Stationary Distributions ◽  
Theoretical Results

This paper discusses the asymptotic behavior of a class of three-species stochastic model with regime switching. Using the Lyapunov function, we first obtain sufficient conditions for extinction and average time persistence. Then, we prove sufficient conditions for the existence of stationary distributions of populations, and they are ergodic. Numerical simulations are carried out to support our theoretical results.

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 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.

scholarly journals Stationary Distribution and Extinction in a Stochastic SIQR Epidemic Model Incorporating Media Coverage and Markovian Switching

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1122
Author(s):  
Yanlin Ding ◽  
Jianjun Jiao ◽  
Qianhong Zhang ◽  
Yongxin Zhang ◽  
Xinzhi Ren
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Function ◽  
Stationary Distribution ◽  
Dynamic Characteristics ◽  
Epidemic Model ◽  
Regime Switching ◽  
Media Coverage ◽  
Sufficient Conditions ◽  
Unique Positive Solution ◽  
Theoretical Results

This paper is concerned with the dynamic characteristics of the SIQR model with media coverage and regime switching. Firstly, the existence of the unique positive solution of the proposed system is investigated. Secondly, by constructing a suitable random Lyapunov function, some sufficient conditions for the existence of a stationary distribution is obtained. Meanwhile, the conditions for extinction is also given. Finally, some numerical simulation examples are carried out to demonstrate the effectiveness of theoretical results.

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