混合随机SIR传染病模型的动力学分析

研究一类具有一般发病率函数的混合随机SIR传染病模型.首先,通过构造适当的Lyapunov函数,证明了模型全局正解的存在唯一性.然后,利用随机分析方法,建立了系统灭绝与持久的充分且几乎必要条件和遍历平稳分布的存在性.最后,通过数值模拟来验证理论结果.     

同时具有logistic出生和Markov切换的随机SIRS传染病模型的动力学

研究了一类同时具有logistic出生和Markov切换的随机SIRS传染病模型.首先通过构造合适的V函数，利用It?公式分析了随机传染病模型全局正解的存在唯一性，继而讨论出了该模型的解存在一个遍历平稳分布的结果，以及疾病灭绝的充分条件，最后给出了数值例子来说明本文得出的结论.     

带有隔离的COVID-19随机SQIR模型研究

本文考虑一类受环境噪声影响,带有隔离的COVID-19随机SQIR传染病模型.通过构造Lyapunov函数并利用It?公式,证明全局正解的存在唯一性;得到决定疾病灭绝、持久和遍历平稳分布的充分条件.结果表明:环境变化在一定条件下会对疾病起抑制作用.最后,通过数值模拟来验证理论结果的正确性.     

一类肠道菌群模型的随机动力学行为

本文研究一类随机肠道菌群模型的动力学行为.应用Lyapunov函数法,首先证明全局正解的存在唯一性及有界性.其次,分别给出菌群灭绝、持久和模型正解存在唯一遍历分布的充分条件.最后通过数值模拟分别检验了结果的正确性.     

Markov调制的随机系统平稳分布的存在与唯一性(英文)

本文讨论Markov调制的随机系统平稳分布的存在与唯一性. 利用Lyapunov方法与耦合方法得到这类系统存在唯一平稳分布的一些充分条件, 这些条件易于验证具可操作性.     

随机环境中受控分枝过程的灭绝概率

本文给出在平稳遍历随机环境下受控分枝过程增长率的一个上界以及过程灭绝的充分条件.     

时滞合作捕食模型的随机动力学分析

本文主要研究了一种带有时滞的三物种模型,其中一个物种以另外两个合作的物种为食物.首先,利用比较原理和随机分析理论,建立了平稳分布的准则;其次,利用初值的假设和比较原理,给出了物种的生存性或者灭绝性的充分条件;最后,结合矩阵理论,得到了解的分布平稳,且弱收敛到唯一的一个遍历不变分布.     

随机生灭Q矩阵的极限谱分布

本文主要研究随机生灭Q矩阵的极限谱分布.在严平稳遍历的情形下,本文证明随机生灭Q矩阵的经验谱分布弱收敛于某个非随机概率分布.进一步,在非严平稳遍历情形下,本文研究了比BetaHermite系综更广的一类随机矩阵模型,建立了与之相应的随机生灭Q矩阵的极限谱分布存在性,并且证明它的极限谱分布具有卷积表达式.特别地,Beta-Hermite系综所对应的随机生灭Q矩阵的极限谱分布是经典半圆率与Dirac测度δ-2的卷积.     

GI/G/1排队系统的几种收敛速度

对随机模型,可以从不同角度研究其稳定性,一种是研究其转移概率函数趋向于平稳分布的速度,即各种遍历性;另一种是研究平稳分布的尾部衰减速度.本文从这两个方面着手,找它们之间的关系,对GI/G/1排队系统,给出等待时间列几何遍历、平稳分布轻尾与服务时间分布轻尾三者等价,l-遍历、平稳分布的尾部(l-1)-阶衰减与服务时间分布的尾部l-阶衰减三者等价,最后证明出等待时间列不是强遍历.     

一类具有常数输入的随机SIR流行病模型的定性分析

研究了一类易感者和恢复者具有常数输入的随机SIR传染病模型.利用停时理论及Lyapunov分析方法,证明了该随机模型正解的全局存在唯一性和有界性,讨论了随机模型的解在相应确定模型的无病平衡点和地方病平衡点附近的振荡行为以及得到了随机模型的解的平均持久和疾病灭绝的充分条件.最后,通过数值模拟验证和理论推导的一致性.     

Dynamics of a Stochastic SIR Epidemic Model with Logistic Growth

In this paper, a stochastic SIR epidemic model with saturated treatment function, non-monotone incidence rate and logistic growth is studied. First, we prove that the stochastic model has a unique global positive solution. Next, by constructing a suitable Lyapunov function, we can show that there exists an ergodic stationary distribution in the random SIR model. Then, we show that a sufficient condition can make the disease tend to extinction. Finally, some numerical simulations are used to prove our analytical result.     

The threshold for a stochastic HIV-1 infection model with Beddington-DeAngelis incidence rate

In this paper, we consider a stochastic HIV-1 infection model with Beddington-DeAngelis incidence rate. Before exploring its long-time behavior we show that there is a global positive solution of this model. Then sufficient conditions for extinction of the disease are established. Moreover, we give sufficient conditions for the existence of a stationary distribution of the model through constructing a suitable stochastic Lyapunov function. The stationary distribution implies that the disease is persistent in the mean. Therefore, a threshold value for the disease to disappear or prevail is obtained. Finally, some numerical examples are illustrated to support our theoretical results.     

Dynamical behavior of a stochastic HBV infection model with logistic hepatocyte growth

This paper is concerned with a stochastic HBV infection model with logistic growth. First, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the HBV infection model. Then we obtain sufficient conditions for extinction of the disease. The stationary distribution shows that the disease can become persistent in vivo.     

Dynamical behavior of a stochastic predator-prey model with stage structure for prey

Abstract

In the present paper, we focus on a stochastic predator-prey model with stage structure for prey. Firstly, by using the stochastic Lyapunov function method, we obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for extinction of the predator population in two cases. Some examples and numerical simulations are carried out to validate our analytical findings.     

Dynamics of a Stochastic Predator–Prey Model with Stage Structure for Predator and Holling Type II Functional Response

In this paper, we develop and study a stochastic predator–prey model with stage structure for predator and Holling type II functional response. First of all, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Then, we obtain sufficient conditions for extinction of the predator populations in two cases, that is, the first case is that the prey population survival and the predator populations extinction; the second case is that all the prey and predator populations extinction. The existence of a stationary distribution implies stochastic weak stability. Numerical simulations are carried out to demonstrate the analytical results.     

Stationary distribution and extinction of a stochastic SIRI epidemic model with relapse

In this paper, we study the dynamics of a stochastic Susceptible-Infective-Removed-Infective (SIRI) epidemic model with relapse. By constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence of an ergodic stationary distribution to the model. Moreover, sufficient conditions for extinction of the disease are also obtained.     

Stationary distribution and extinction of a stochastic nutrient-phytoplankton-zooplankton model with cell size

In this paper, we study a stochastic nutrient-phytoplankton-zooplankton model with cell size that represents the interaction between internal mechanism of species and external environment. We first investigate the existence and uniqueness of the global positive solution with positive initial values. Then we construct sufficient conditions for the existence of an ergodic stationary distribution of positive solution. Once more, we find that large noise intensities cause the extinctions of phytoplankton and zooplankton. Finally, numerical simulations are given to verify the correctness of theoretical results.     

Stationary distribution and extinction of a stochastic one-prey two-predator model with Holling type II functional response

In this article, we investigate a stochastic one-prey two-predator model with Holling type II functional response. We first establish sufficient conditions for persistence and extinction of prey and predator populations, then by constructing a suitable stochastic Lyapunov function, we establish sharp sufficient criteria for the existence of a unique ergodic stationary distribution of the positive solutions to the model. The results show that the smaller white noise can ensure the persistence of prey and predator populations while the larger white noise can lead to the extinction of prey and predator populations.     

Stationary distribution and extinction of a stochastic predator–prey model with distributed delay

In this paper, we focus on a stochastic predator–prey model with distributed delay. We first obtain the existence of a stationary distribution to the positive solutions by stochastic Lyapunov function method. Then we establish sufficient conditions for extinction of the predator population, that is, the prey population is survival and the predator population is extinct.     

Stationary Distribution and Extinction of Stochastic HTLV-I Infection Model with CTL Immune Response under Regime Switching

In this paper, the stochastic HTLV-I infection model with CTL immune response is investigated. Firstly, we show that the stochastic system exists unique positive global solution originating from the positive initial value. Secondly, we obtain that the existence of ergodic stationary distribution of the model by stochastic Lyapunov functions. Thirdly, we establish sufficient conditions for extinction of the infected cells. Finally, numerical simulations are carried out to illustrate the theoretical results.