DYNAMICAL BEHAVIOR OF STOCHASTIC COMPETITION BETWEEN PLASMID-BEARING AND PLASMID-FREE ORGANISMS IN A CHEMOSTAT MODEL

Stochastic Characteristics

In this paper, a model of stochastic competition between plasmid-bearing and plasmid-free organisms in a chemostat is investigated. First, we show that there is a unique global positive solution for the stochastic system. Second, by employing stochastic Lyapunov functions, Itô formula, strong law of large number and some other important inequalities, stochastic characteristics of the stochastic competition chemostat model are studied such as the stochastic asymptotic behaviors of the system. Finally, some numerical simulations are given.

Dynamical Behavior of a Stochastic SIRC Model for Influenza A

Symmetry ◽

10.3390/sym12050745 ◽

2020 ◽

Vol 12 (5) ◽

pp. 745 ◽

Cited By ~ 1

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 ◽

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.

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

Advances in Difference Equations ◽

10.1186/s13662-019-2352-5 ◽

2019 ◽

Vol 2019 (1) ◽

Cited By ~ 3

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.

Dynamics of a stochastic SIQR epidemic model with saturated incidence rate

Filomat ◽

10.2298/fil1815239w ◽

2018 ◽

Vol 32 (15) ◽

pp. 5239-5253 ◽

Cited By ~ 3

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 ◽

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.

Dynamics of an autonomous Gilpin–Ayala competition model with random perturbation

10.1142/s1793524520500436 ◽

2021 ◽

pp. 2050043

Author(s):

Jing Fu ◽

Qixing Han ◽

Daqing Jiang ◽

Yanyan Yang

Keyword(s):

White Noise ◽

Numerical Simulations ◽

Positive Solution ◽

Necessary Conditions ◽

Random Perturbation ◽

Sufficient Conditions ◽

Competition Model ◽

Interacting Species ◽

Sufficient And Necessary Conditions ◽

Global Positive Solution

This paper discusses the dynamics of a Gilpin–Ayala competition model of two interacting species perturbed by white noise. We obtain the existence of a unique global positive solution of the system and the solution is bounded in [Formula: see text]th moment. Then, we establish sufficient and necessary conditions for persistence and the existence of an ergodic stationary distribution of the model. We also establish sufficient conditions for extinction of the model. Moreover, numerical simulations are carried out for further support of present research.

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

10.1142/s1793524521500443 ◽

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 ◽

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

10.1142/s1793524521500327 ◽

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 ◽

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.

Dynamics of a stochastic periodic SIRS model with time delay

10.1142/s1793524520500722 ◽

2020 ◽

pp. 2050072

Author(s):

Xiangyun Shi ◽

Yimeng Cao

Keyword(s):

Time Delay ◽

Numerical Simulations ◽

Epidemic Model ◽

Lyapunov Functions ◽

Ultimate Boundedness ◽

Sirs Epidemic Model ◽

Dynamical Behaviors ◽

Sirs Model ◽

Stochastically Ultimate Boundedness

Dynamical behaviors of a stochastic periodic SIRS epidemic model with time delay are investigated. By constructing suitable Lyapunov functions and applying Itô’s formula, the existence of the global positive solution and the property of stochastically ultimate boundedness of model (1.1) are proved. Moreover, the extinction and the persistence of the disease are established. The results are verified by numerical simulations.

Asymptotic behavior of a stochastic HIV model with Beddington–DeAngelis functional response

Advances in Difference Equations ◽

10.1186/s13662-020-02911-7 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Suxia Wang ◽

Juan Zhao ◽

Junxing Zhu ◽

Xiaoli Ren

Keyword(s):

Asymptotic Behavior ◽

Steady State ◽

Numerical Simulations ◽

Positive Solution ◽

Functional Response ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Hiv Model ◽

Stochastically Stable ◽

Global Positive Solution

Abstract In this paper, we study the dynamics property of a stochastic HIV model with Beddington–DeAngelis functional response. It has a unique uninfected steady state. We prove that the model has a unique global positive solution. Furthermore, if the basic reproductive number is not larger than 1, the asymptotic behavior of the solution is stochastically stable. Otherwise, it fluctuates randomly around the infected steady state of the corresponding deterministic HIV model. Finally, some numerical simulations are carried out to verify our results.

Dynamics of delayed stochastic predator–prey models with feedback controls based on discrete observations

10.1142/s1793524517500401 ◽

2017 ◽

Vol 10 (03) ◽

pp. 1750040 ◽

Cited By ~ 1

Author(s):

Dianli Zhao ◽

Sanling Yuan

Keyword(s):

Numerical Simulations ◽

Stochastic System ◽

Necessary Conditions ◽

Deterministic Model ◽

Sufficient Conditions ◽

Discrete Observations ◽

Feedback Controls ◽

Predator Prey ◽

Predator Prey Models

In this paper, we concern a class of the generalized delayed stochastic predator–prey models with feedback controls based on discrete observations. The existence of global positive solution is given first. Then we discuss the deterministic model briefly, and establish the necessary conditions and the sufficient conditions for almost-sure extinction and persistence in mean for the stochastic system, where we show that the feedback controls can change the properties of the population systems significantly. Finally, numerical simulations are introduced to support the main results.

Periodic solution of the DS-I-A epidemic model with stochastic perturbations

Filomat ◽

10.2298/fil1908219l ◽

2019 ◽

Vol 33 (8) ◽

pp. 2219-2235

Author(s):

Songnan Liu ◽

Xiaojie Xu

Keyword(s):

Periodic Solution ◽

Stochastic Model ◽

Positive Solution ◽

Stochastic System ◽

Epidemic Model ◽

Lyapunov Functions ◽

Positive Periodic Solution ◽

Unique Positive Solution ◽

Stochastic Perturbations ◽

Analytical Results

The paper introduces DS-I-A model with periodical coefficients. First of all, we show that there is a unique positive solution of the stochastic model. Furthermore we deduce the conditions under which the disease will end and continue. At last, we draw a conclusion that there exists nontrivial positive periodic solution for the stochastic system by stochastic Lyapunov functions. Simulations are also carried out to confirm our analytical results.