Uniform Persistence, Periodicity and Extinction in a Delayed Biological System with Stage Structure and Density-Dependent Juvenile Birth Rate

A delayed biological system of predator-prey interaction with stage structure and density dependent juvenile birth rate is investigated. It is assumed that the prey population has two stages: immature and mature. The growth of the immature prey is density dependent and is a function of the density of adult prey. Such phenomenon has been reported for beetles, tribolium, copepods, scorpions, several fish species and even crows. The growth of the predator is affected by the time delay due to gestation. By some Lemmas and methods of delay differential equation, the conditions for the uniform persistence and extinction of the system are obtained. Numerical simulations illustrate the feasibility of the main results and demonstrate that the density dependent coefficient has influence on the system populations’ densities though it has no effect on uniform persistence and extinction of the system.

Persistence and Extinction in Two Species Models with Impulse

Both uniform persistence and global extinction are established for a two species predatorprey and competition system with impulse by appealing to theories of abstract persistence, asymptotically autonomous semiflows, and the comparison theorem.

Persistence and extinction of Markov switched stochastic Nicholson’s blowflies delayed differential equation

In this paper,we study the persistence and extinction of Markov switched stochastic Nicholson's blowflies delayed differential equation.We derive sufficient conditions of persistence and extinction for blowflies population,respectively,which solve one of open problems proposed by Zhu et al.

PERSISTENCE AND EXTINCTION OF A STOCHASTIC SIS EPIDEMIC MODEL WITH DOUBLE EPIDEMIC HYPOTHESIS

In this paper, we aim at dynamical behaviors of a stochastic SIS epidemic model with double epidemic hypothesis. Sufficient conditions for the extinction and persistence in mean are derived via constructing suitable functions. We obtain a threshold of stochastic SIS epidemic model, which determines how the diseases spread when the white noises are small. Numerical simulations are used to illustrate the efficiency of the main results of this article.

PERSISTENCE, EXTINCTION AND STABILITY FOR NONLINEAR PLANKTON ALLELOPATHY MODEL WITH DELAYED NEGATIVE FEEDBACKS

By the techniques of comparison argument and Lyapunov-like functionals, some criteria about persistence and extinction of the species are obtained. And then, with the help of constructing Lyapunov functionals and some new analysis method, sufficient conditions, provided with the form of average value of a function, to guarantee the stability of the system are derived. Finally, some examples together with their numerical simulations show the feasibility of these main results. Our conclusions are different from many existing forms for nonlinear competitive systems.

具有避难所和Ornstein-Uhlenbeck过程的随机三种群捕食模型的持久与灭绝

目前大多数的捕食模型都是用白噪声描述环境的随机性,针对真实情境下,模型中的参数可能满足Ornstein-Uhlenbeck过程的问题,提出具有避难所和Ornstein-Uhlenbeck过程的随机三种群捕食模型。利用伊藤公式、微分不等式及随机分析理论对模型进行动力学行为分析。证明了模型全局正解的存在唯一性,分别得到了每个种群平均持久生存和灭绝的充分条件,最后利用python进行数值模拟,验证了定理中所得到的结论,并进一步研究了避难所对种群数量的影响。

受媒体信息影响的一类随机传染病模型的研究

考虑到媒体信息对疾病预防和控制具有重要作用,建立了一类受媒体信息影响和具有非线性传染率的随机SEIS传染病模型,并运用随机微分方程的相关理论研究了该模型的绝灭性、持久性和平稳分布.数值模拟验证表明,当环境随机干扰越强或媒体信息报道得越及时时,传染病的绝灭速度越快.该研究结果改进和丰富了文献[12]的相关研究结果,并可为利用媒体信息进行预防和控制疾病提供良好参考。

一类随机SWEIA艾滋病毒传播模型的动力学分析

研究了一类具有随机效应的SWEIA艾滋病毒传播模型.首先,通过构造Lyapunov函数证明了确定性模型平衡点的全局渐近稳定性,利用停顿理论等方法证明了随机模型正解的全局存在唯一性与有界性;其次,分析了随机模型的解在相应确定性模型的无病平衡点与地方病平衡点附近的震荡行为,并得到了随机模型解的平均持续与灭绝性的充分条件;最后,通过数值模拟进一步显示了模型的动力学行为.

具有心理效应和媒体影响的随机HIV/AIDS传染病模型

建立了一类满足Logistic人口增长方程且同时具有心理效应和媒体影响的随机HIV/AIDS传染病模型,通过构造相应的Lyapunov函数,利用停时理论、伊藤引理及强大数定理等对随机HIV/AIDS传染病模型进行了理论分析,进而证明了随机模型全局正解的存在唯一性,并且通过对相应Lyapunov函数的计算研究,给出了疾病灭绝和持久的充分条件.最后,利用最小二乘法和Euler-Maruyama方法对随机传染病模型进行数值模拟,进一步显示了随机传染病模型的动力学行为.

一类随机SEIAQR腮腺炎传染病模型的动力学分析

为探究现实环境中随机因素对腮腺炎传播的影响,研究了一类具有随机效应的SEIAQR腮腺炎传染病模型。首先凭借停时理论证明了随机模型全局正解的存在唯一性,并通过构造Lyapunov函数并引入It8公式,分析了随机模型的解在相应确定性模型的无病平衡点和地方病平衡点附近的震荡行为;然后探究了随机模型解的平均持续性以及疾病灭绝的充分条件;最后通过数值模拟添加了噪声对模型的影响。结果显示:随机模型在确定性模型的平衡点附近扰动,扰动程度和噪声强度呈正相关,充分大的噪声会使疾病灭绝。

觅食竞技场下浮游生物模型的动力学行为

主要讨论觅食竞技场下浮游生物的动力学行为。证明对于任意给定的正初始值,系统都存在唯一的全局正解;应用随机微分方程的比较定理,得到系统持久与灭绝的充分条件,并且证明系统具有一个唯一的遍历平稳分布。最后,用数值模拟验证了理论结果。

具有恐惧效应和Holling Ⅲ功能性反应的随机捕食-食饵系统

该文研究了一类具有恐惧效应和Holling Ⅲ功能反应的随机捕食-食饵系统.首先,证明了在任意给定正初始值下,系统全局正解的存在唯一性与均值有界性及随机最终有界性;其次,研究了食饵种群和捕食者种群灭绝和平均持续生存的充分条件,并构造Lyapunov函数证明了系统存在平稳分布及遍历性;最后,通过数值模拟验证了文章的结果.

Numerical Analysis of Bacterial Meningitis Stochastic Delayed Epidemic Model through Computational Methods

Based on theWorld Health Organization(WHO),Meningitis is a severe infection of the meninges,the membranes covering the brain and spinal cord.It is a devastating disease and remains a significant public health challenge.This study investigates a bacterial meningitis model through deterministic and stochastic versions.Four-compartment population dynamics explain the concept,particularly the susceptible population,carrier,infected,and recovered.The model predicts the nonnegative equilibrium points and reproduction number,i.e.,the Meningitis-Free Equilibrium(MFE),and Meningitis-Existing Equilibrium(MEE).For the stochastic version of the existing deterministicmodel,the twomethodologies studied are transition probabilities and non-parametric perturbations.Also,positivity,boundedness,extinction,and disease persistence are studiedrigorouslywiththe helpofwell-known theorems.Standard and nonstandard techniques such as EulerMaruyama,stochastic Euler,stochastic Runge Kutta,and stochastic nonstandard finite difference in the sense of delay have been presented for computational analysis of the stochastic model.Unfortunately,standard methods fail to restore the biological properties of the model,so the stochastic nonstandard finite difference approximation is offered as an efficient,low-cost,and independent of time step size.In addition,the convergence,local,and global stability around the equilibria of the nonstandard computational method is studied by assuming the perturbation effect is zero.The simulations and comparison of the methods are presented to support the theoretical results and for the best visualization of results.

模型化益生菌对治疗前列腺癌的潜在影响

根据益生菌与前列腺癌细胞之间的相互作用机制,构建了由益生菌、雄性激素依赖性前列腺癌细胞和雄性激素非依赖性前列腺癌细胞组成的三维随机癌动力学模型.通过构建V函数,获得了前列腺癌细胞持续、灭绝的充分条件.模拟预测了益生菌辅助雄性激素剥夺疗法治疗前列腺癌的效果.研究表明:益生菌对前列腺癌细胞的抑制作用和噪声强度在前列腺癌细胞持续和灭绝中扮演了重要作用;增强噪声强度或改进有益菌对癌细胞的抑制作用不仅可以有效根除癌细胞而且可以有效防止耐药现象的发生.

一类具有垂直传染的随机SIS模型的稳定性

研究一类具有饱和发生率和垂直传染的随机SIS传染病模型,分别考虑外部环境对于易感者和染病者出生率、死亡率的扰动,证明了模型存在唯一的全局正解,通过构造Lyapunov函数证明了传染病的灭绝,得到疾病持久的充分条件。

一类随机时滞竞争模型的动力学分析

建立了生长率与捕获努力量均受到白噪声干扰的两种群随机时滞竞争模型,利用随机分析理论得到了种群灭绝与在均值意义下持久的充分条件,并给出数值模拟以验证所得到结果.

具有非线性发生率及两个独立扰动的SIS传染病模型的动力学分析

研究具有两类随机扰动且具有非线性发生率的SIS传染病模型,通过构造Lyapunov函数方法证明了在一定条件下模型正解的存在唯一性,得到关于感染种群趋于灭绝和保持持久的充分条件,证明了平稳分布的存在并给出了数值模拟结果.

带有Ornstein-Uhlenbeck过程的随机logistic种群模型

研究带有均值回复Ornstein-Uhlenbeck过程的随机logistic种群模型的动力学行为。证明收获努力E可以控制随机微分方程模型的随机灭绝和持续:若E≥E^(*)并且满足一些其他条件,则种群灭绝;若E<E,则种群持续。同时得到小的回复速率θ或大的波动强度ξ会抑制种群增长,大的回复速率θ或小的波动强度ξ有利于种群增长。

一类随机SICR丙肝模型的动力学分析

为了研究现实中不确定因素对丙肝的影响,考虑了一类具有急性与慢性感染的随机SICR丙肝模型。首先,依据停时理论证明了全局正解的存在唯一性;其次,通过构造Lyapunov函数并结合伊藤公式,讨论了随机模型的解在确定模型的无病平衡点和正平衡点附近的振荡行为,并给出了随机模型解的平均持续和疾病灭绝的充分条件。最后,数值模拟考虑了噪声对模型的影响,结果表明:随机模型在确定模型的平衡点附近扰动,扰动强度与噪声强度成正相关,并且足够大的噪声使疾病灭绝,进一步证实了理论结果。

Persistence and periodic measure of a stochastic predator-prey model with Beddington-DeAngelis functional response

In this paper,we study a stochastic predator-prey model with Beddington-DeAngelis functional response and time-periodic coefficients.By analyzing the stability of the solution on the boundary and some stochastic estimates,the threshold conditions for the time-average persistence in probability and extinction of each population are established.Furthermore,the existence of a unique periodic measure of the model is also presented under the condition of the time-average persistence in probability of the model.Several numerical simulations are given to verify the effectiveness of the theoretical results and to illustrate the effects of the white noises on the persistence and periodic measure of the model.