scholarly journals Ergodicity of a Nonlinear Stochastic SIRS Epidemic Model with Regime-Switching Diffusions

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Hongxia Liu ◽  
Juan Li ◽  
Mengnan Chi ◽  
Jinlei Liu ◽  
Wencai Zhao
Keyword(s):  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
Threshold Parameter ◽  
Sirs Epidemic Model ◽  
Switching Diffusions ◽  
White Noises ◽  
Stochastic Sirs Epidemic Model

In this paper, taking both white noises and colored noises into consideration, a nonlinear stochastic SIRS epidemic model with regime switching is explored. The threshold parameter R s is found, and we investigate sufficient conditions for the existence of the ergodic stationary distribution of the positive solution. Finally, some numerical simulations are also carried out to demonstrate the analytical results.

scholarly journals Dynamics of a Stochastic SIRS Epidemic Model with Regime Switching and Specific Functional Response

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Amine EL Koufi ◽  
Abdelkrim Bennar ◽  
Noura Yousfi
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Regime Switching ◽  
Unique Positive Solution ◽  
Sirs Epidemic Model ◽  
Sirs Model ◽  
Incident Rate ◽  
Stochastic Sirs Epidemic Model

The purpose of this work is to investigate the dynamic behaviors of the SIRS epidemic model with nonlinear incident rate under regime switching. We establish the existence of a unique positive solution of our system. Furthermore, we obtain the conditions for the extinction of diseases, and we show the existence of the stationary distribution for our stochastic SIRS model under regime switching. Numerical simulations are employed to illustrate our theoretical analysis.

Dynamics of a stochastic SIRS epidemic model with standard incidence under regime switching

2021 ◽  
pp. 2150074
Author(s):  
Jiang Xu ◽  
Yinong Wang ◽  
Zhongwei Cao
Keyword(s):  
Lyapunov Function ◽  
Stochastic System ◽  
Epidemic Model ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
Sirs Epidemic Model ◽  
Persistence In The Mean ◽  
The Mean ◽  
Stochastic Sirs Epidemic Model ◽  
Stochastic Lyapunov Function

The goal of this paper is to introduce and initiate a study of a stochastic SIRS epidemic model with standard incidence which is perturbed by both white and telegraph noises. We first show persistence in the mean and then establish the sufficient conditions for extinction of the disease. Moreover, in the case of persistence, we obtain sufficient conditions for the existence of positive recurrence of the solutions by means of structuring suitable stochastic Lyapunov function with regime switching. Meanwhile, the threshold between persistence in the mean and extinction of the stochastic system is also obtained. Finally, we test our theory conclusion by simulations.

Dynamics of a stochastic susceptible-infective-recovered (SIRS) epidemic model with vaccination and nonlinear incidence under regime switching and Lévy jumps

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Junna Hu ◽  
Buyu Wen ◽  
Ting Zeng ◽  
Zhidong Teng
Keyword(s):  
Epidemic Model ◽  
Regime Switching ◽  
Markov Switching ◽  
Threshold Value ◽  
Open Problems ◽  
Nonlinear Incidence ◽  
Sirs Epidemic Model ◽  
Stochastic Epidemic ◽  
Lévy Jumps ◽  
White Noises

Abstract In this paper, a stochastic susceptible-infective-recovered (SIRS) epidemic model with vaccination, nonlinear incidence and white noises under regime switching and Lévy jumps is investigated. A new threshold value is determined. Some basic assumptions with regard to nonlinear incidence, white noises, Markov switching and Lévy jumps are introduced. The threshold conditions to guarantee the extinction and permanence in the mean of the disease with probability one and the existence of unique ergodic stationary distribution for the model are established. Some new techniques to deal with the Markov switching, Lévy jumps, nonlinear incidence and vaccination for the stochastic epidemic models are proposed. Lastly, the numerical simulations not only illustrate the main results given in this paper, but also suggest some interesting open problems.

A stochastic vaccinated epidemic model incorporating Lévy processes with a general awareness-induced incidence

2021 ◽  
pp. 2150044
Author(s):  
Khadija Akdim ◽  
Adil Ez-Zetouni ◽  
Mehdi Zahid
Keyword(s):  
Numerical Simulations ◽  
Positive Solution ◽  
Dynamic Behavior ◽  
Epidemic Model ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Lévy Noise ◽  
Global Positive Solution ◽  
Levy Noise ◽  
Disease Free

In this paper, we investigate a stochastic vaccinated epidemic model with a general awareness-induced incidence perturbed by Lévy noise. First, we show that this model has a unique global positive solution. Therefore, we establish the dynamic behavior of the solution around both disease-free and endemic equilibrium points. Furthermore, when [Formula: see text], we give sufficient conditions for the existence of an ergodic stationary distribution to the model when the jump part in the Lévy noise is null. Finally, we present some examples to illustrate the analytical results by numerical simulations.

Dynamics of a stochastic rabies epidemic model with markovian switching

2021 ◽  
pp. 2150032
Author(s):  
Hao Peng ◽  
Xinhong Zhang ◽  
Daqing Jiang
Keyword(s):  
Lyapunov Function ◽  
White Noise ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Telegraph Noise ◽  
Global Positive Solution ◽  
Theoretical Results

In this paper, we analyze a stochastic rabies epidemic model which is perturbed by both white noise and telegraph noise. First, we prove the existence of the unique global positive solution. Second, by constructing an appropriate Lyapunov function, we establish a sufficient condition for the existence of a unique ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for the extinction of diseases. Finally, numerical simulations are introduced to illustrate our theoretical results.

scholarly journals Dynamical Behavior of a Stochastic SIRC Model for Influenza A

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 745 ◽  
Author(s):  
Tongqian Zhang ◽  
Tingting Ding ◽  
Ning Gao ◽  
Yi Song
Keyword(s):  
Lyapunov Function ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Influenza A ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Global Positive Solution ◽  
Theoretical Results ◽  
Stochastic Lyapunov Function

In this paper, a stochastic SIRC epidemic model for Influenza A is proposed and investigated. First, we prove that the system exists a unique global positive solution. Second, the extinction of the disease is explored and the sufficient conditions for extinction of the disease are derived. And then the existence of a unique ergodic stationary distribution of the positive solutions for the system is discussed by constructing stochastic Lyapunov function. Furthermore, numerical simulations are employed to illustrate the theoretical results. Finally, we give some further discussions about the system.

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 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.

scholarly journals Dynamics of a stochastic SIQR epidemic model with saturated incidence rate

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5239-5253 ◽  
Author(s):  
Li-Li Wang ◽  
Nan-Jing Huang ◽  
Donal O’Regan
Keyword(s):  
Numerical Simulations ◽  
Positive Solution ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Global Positive Solution ◽  
The Mean

The purpose of this paper is to propose and investigate a stochastic SIQR epidemic model with saturated incidence rate. Firstly, we give some conditions to guarantee the stochastic SIQR epidemic model has a unique global positive solution. Then we verify that the disease in this model will die out exponentially if Rs 0 < 1, while the disease will be persistent in the mean if Rs 0 > 1. Moreover, by constructing suitable Lyapunov functions, we establish some sufficient conditions for the existence of an ergodic stationary distribution for the model. Finally, we provide some numerical simulations to illustrate the analytical results.

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