Global dynamical behavior of a multigroup SVIR epidemic model with Markovian switching

2021 ◽  
pp. 2150080
Author(s):  
Qun Liu ◽  
Daqing Jiang
Keyword(s):  
Markov Process ◽  
Lyapunov Function ◽  
Stochastic System ◽  
Epidemic Model ◽  
Regime Switching ◽  
Dynamical Behavior ◽  
Piecewise Deterministic Markov Process ◽  
Positive Recurrence ◽  
Persistence In The Mean ◽  
The Mean

In this paper, we are concerned with the global dynamical behavior of a multigroup SVIR epidemic model, which is formulated as a piecewise-deterministic Markov process. We first obtain sufficient criteria for extinction of the diseases. Then we establish sufficient criteria for persistence in the mean of the diseases. Moreover, in the case of persistence, we find a domain which is positive recurrence for the solution of the stochastic system by constructing an appropriate Lyapunov function with regime switching.

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.

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.

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.

Study on a susceptible–infected–vaccinated model with delay and proportional vaccination

2018 ◽  
Vol 11 (08) ◽  
pp. 1850102 ◽  
Author(s):  
Shuqi Gan ◽  
Fengying Wei
Keyword(s):  
Positive Solution ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Stochastic Epidemic ◽  
Persistence In The Mean ◽  
Global Positive Solution ◽  
The Mean ◽  
Stochastic Epidemic Model

A susceptible–infected–vaccinated epidemic model with proportional vaccination and generalized nonlinear rate is formulated and investigated in the paper. We show that the stochastic epidemic model admits a unique and global positive solution with probability one when constructing a proper [Formula: see text]-function therewith. Then a sufficient condition that guarantees the disappearances of diseases is derived when the indicator [Formula: see text]. Further, if [Formula: see text], then we obtain that the solution is weakly permanent with probability one. We also derived the sufficient conditions of the persistence in the mean for the susceptible and infected when another indicator [Formula: see text].

Dynamical behaviors of a prey-predator model with foraging arena scheme in polluted environments

2021 ◽  
Vol 71 (1) ◽  
pp. 235-250
Author(s):  
Xin He ◽  
Xin Zhao ◽  
Tao Feng ◽  
Zhipeng Qiu
Keyword(s):  
Periodic Solution ◽  
Stochastic System ◽  
Sufficient Conditions ◽  
Numerical Examples ◽  
Dynamical Behaviors ◽  
Analytical Results ◽  
Persistence In The Mean ◽  
The Mean ◽  
Predator Model

Abstract In this paper, a stochastic prey-predator model is investigated and analyzed, which possesses foraging arena scheme in polluted environments. Sufficient conditions are established for the extinction and persistence in the mean. These conditions provide a threshold that determines the persistence in the mean and extinction of species. Furthermore, it is also shown that the stochastic system has a periodic solution under appropriate conditions. Finally, several numerical examples are carried on to demonstrate the analytical results.

A generalized stochastic competitive system with Ornstein–Uhlenbeck process

2020 ◽  
pp. 2150001
Author(s):  
Baodan Tian ◽  
Liu Yang ◽  
Xingzhi Chen ◽  
Yong Zhang
Keyword(s):  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Competitive System ◽  
Uhlenbeck Process ◽  
Stochastic Perturbations ◽  
Stochastic Permanence ◽  
Persistence In The Mean ◽  
Ornstein Uhlenbeck Process ◽  
Global Positive Solution ◽  
The Mean

A generalized competitive system with stochastic perturbations is proposed in this paper, in which the stochastic disturbances are described by the famous Ornstein–Uhlenbeck process. By theories of stochastic differential equations, such as comparison theorem, Itô’s integration formula, Chebyshev’s inequality, martingale’s properties, etc., the existence and the uniqueness of global positive solution of the system are obtained. Then sufficient conditions for the extinction of the species almost surely, persistence in the mean and the stochastic permanence for the system are derived, respectively. Finally, by a series of numerical examples, the feasibility and correctness of the theoretical analysis results are verified intuitively. Moreover, the effects of the intensity of the stochastic perturbations and the speed of the reverse in the Ornstein–Uhlenbeck process to the dynamical behavior of the system are also discussed.

scholarly journals Dynamics of a stochastic phytoplankton-toxic phytoplankton-zooplankton system under regime switching

2021 ◽  
Author(s):  
He Liu ◽  
Chuanjun Dai ◽  
Hengguo Yu ◽  
Qing Guo ◽  
Jianbing Li ◽  
...  
Keyword(s):  
White Noise ◽  
Regime Switching ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Aquatic Environments ◽  
Combined Effects ◽  
Toxic Phytoplankton ◽  
Persistence In The Mean ◽  
Global Positive Solution ◽  
The Mean

In this paper, a stochastic phytoplankton-toxic phytoplankton-zooplankton system with Beddington-DeAngelis functional response, where both the white noise and regime switching are taken into account, is studied analytically and numerically. The aim of this research is to study the combined effects of the white noise, regime switching and toxin-producing phytoplankton (TPP) on the dynamics of the system. Firstly, the existence and uniqueness of global positive solution of the system is investigated. Then some sufficient conditions for the extinction, persistence in the mean and the existence of a unique ergidoc stationary distribution of the system are derived. Significantly, some numerical simulations are carried to verify our analytical results, and show that high intensity of white noise is harmful to the survival of plankton populations, but regime switching can balance the different survival states of plankton populations and decrease the risk of extinction. Additionally, it is found that an increase in the toxin liberation rate produced by TPP will increase the survival change of phytoplankton, while it will reduce the biomass of zooplankton. All these results may provide some insightful understanding on the dynamics of phytoplankton-zooplankton system in randomly disturbed aquatic environments.

scholarly journals Permanence and Extinction of Stochastic Logistic System with Feedback Control under Regime Switching

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Hongxiao Hu ◽  
Ling Zhu
Keyword(s):  
Feedback Control ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Persistence In The Mean ◽  
The Mean

We study a stochastic logistic system with feedback control under regime switching. Sufficient conditions for extinction, non-persistence in the mean, weak persistence, and persistence in the mean are established. A very important fact is found in our results; that is, the feedback control is harmless to the permanence of species even under the regime switching and stochastic perturbation environments. Finally, some examples are introduced to illustrate the main results.

The global dynamics of stochastic Holling type II predator-prey models with non constant mortality rate

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5811-5825
Author(s):  
Xinhong Zhang
Keyword(s):  
Mortality Rate ◽  
Stochastic Model ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Global Dynamics ◽  
Type Ii ◽  
Predator Prey ◽  
Persistence In The Mean ◽  
The Mean ◽  
Predator Prey Models

In this paper we study the global dynamics of stochastic predator-prey models with non constant mortality rate and Holling type II response. Concretely, we establish sufficient conditions for the extinction and persistence in the mean of autonomous stochastic model and obtain a critical value between them. Then by constructing appropriate Lyapunov functions, we prove that there is a nontrivial positive periodic solution to the non-autonomous stochastic model. Finally, numerical examples are introduced to illustrate the results developed.

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.

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