OPTIMAL CONTROL INTERVENTION STRATEGIES USING AN N‐PATCH WATERBORNE DISEASE MODEL

Waterborne diseases are an important concern in public health, especially in communities with limited access to clean water. Different community subpopulations can require different copping strategies for the same diseases. Modeling is one method to assist understanding and the development of effective strategies. To this end, we investigated the use of meta‐population models with three types of control interventions: vaccination, treatment, and water purification. Important mathematical features of the model are determined and examined. Optimal control, applied to the model, is also formulated to determine the effective strategies to reduce the spread of the disease. For example, using optimal control, a four‐fold reduction in infected individuals is possible. The value of such an improvement to the communities involved would be significant.     

GLOBAL STABILITY OF AN SVIR EPIDEMIC MODEL WITH VACCINATION

In this paper, an SIR epidemic model with vaccination for both the newborns and susceptibles is investigated, where it is assumed that the vaccinated individuals have the temporary immunity. The basic reproduction number determining the extinction or persistence of the infection is found. By constructing a Lyapunov function, it is proved that the disease free equilibrium is globally stable when the basic reproduction number is less than or equal to one, and that the endemic equilibrium is globally stable wh...     

GLOBAL ANALYSIS OF SIS EPIDEMIC MODEL WITH A SIMPLE VACCINATION AND MULTIPLE ENDEMIC EQUILIBRIA

An SIS epidemic model with a simple vaccination is investigated in this article. The efficiency of vaccine, the disease-related death rate and population dynamics are also considered in this model. The authors find two threshold R0 and Rc (Rc may not exist). There is a unique endemic equilibrium for R0 > 1 or Rc = R0; there are two endemic equilibria for Rc < R0 < 1; and there is no endemic equilibrium for R0 < Rc < 1. When Rc exists, there is a backward bifurcation from the disease-free equilibrium for R0 = 1. They analyze the stability of equilibria and obtain the globally dynamic behaviors of the model. The results acquired in this article show that an accurate estimation of the efficiency of vaccine is necessary to prevent and controll the spread of disease.     

带接种疫苗和二次感染的年龄结构MSEIR流行病模型分析

本文讨论带二次感染和接种疫苗的年龄结构MSEIR流行病模型。在常数人口规模的假设下,运用微分方程和积分方程中的理论和方法,得到一个与接种疫苗策略ψ有关的再生数R(ψ)的表达式,证明了当R(ψ)<1时,无病平衡态是局部渐近稳定的;当R(ψ)>1时,无病平衡态是不稳定的,此时存在一个地方病平衡态,并且证明当R(0)<1时,无病平衡态是全局渐近稳定的。     

QUALITATIVE ANALYSIS OF AN EPIDEMIC MODEL WITH VACCINATION

An SIRS epidemic modei with vaccination, temporary immunity and vary-ing total population size is considered. The threshold of existence of endemic equilibrium is found. The disease-free equilibrium is globally asymptotically stable below the threshold, the endemic equilibrium is globally asymptotically stable above the threshold.     

多重时滞富营养化生态模型的稳定性与分支分析

本文研究了多重时滞富营养化生态模型的稳定性与分支问题.利用特征值方法,分别研究了具有单时滞和双时滞模型的线性稳定性.发现当模型中的时滞经过一系列临界值时,模型在平衡点附近经历了Hopf分支和Hopf-zero分支,并给出Hopf分支和Hopf-zero分支存在的充分条件.最后数值模拟验证了理论结果.     

带随机过程的随机规划问题最优解集的过程特性与稳定性

本文证明了带随机过程的随机规划问题最优解集做为集值随机过程的可测性、可测最优解选择过程的存在性。研究了最优解集过程的平稳性、马氏性以及最优值过程的鞅性和最优解集过程的集值鞅性。最后，讨论了在有限维分布意义下最优解集过程对所含随机过程参数的连续性以及最优值过程的稳定性。     

A QUALITATIVE ANALYSIS OF A VACCINATION MODEL OF HIV/AIDS WITH STAGED PROGRESSION AND AMELIORATION

An epidemic vaccination model with multiple stages of infection is presented and analyzed. The model allows infected individuals to move from advanced stages of infection back to less advanced stages of infection. A threshold parameter which determines the local stability of the disease-free equilibrium is found. The existence and stability of endemic equilibrium for 2-dimensional phase space are analyzed. At the same time, we put forward an optimal vaccine efficacy.     

一类具有垂直传染与脉冲免疫的SEIR传染病模型的全局分析

考虑了一个具有垂直传染与积分时滞的SEIR传染病动力学模型.分析了该模型在脉冲免疫接种条件下的动力学行为,获得了传染病灭绝的充分条件,进而运用脉冲时滞泛函微分方程理论,获得了含有时滞的系统持久性的充分条件,并且证明了积分时滞与脉冲免疫能对模型的动力学行为产生显著的影响.     

MATHEMATICAL ANALYSIS OF WEST NILE VIRUS MODEL WITH DISCRETE DELAYS

The paper presents the basic model for the transmission dynamics of West Nile virus (WNV). The model, which consists of seven mutually-exclusive compartments representing the birds and vector dynamics,...     

STABILITY ANALYSIS OF H-R NEURON MODEL WITH FRACTIONAL ORDERS

In this paper,we are concerned with a Hindmarsh-Rose(H-R) neuron model of fractional orders.By employing stability theory,we present some sufficient conditions ensuring the equilibrium of system to be stable.The simulations are provided to verify the theoretical results.     

火炮炮口振动模型的统计与优化分析

本文通过对CCD测量设备测量火炮射击时炮口振动位移数据的分析，提出了描述火炮射击时他口的振动位移的数学模型用该模型拟合测量的振动位移数据表明，我们的模型具有良好的拟合度．利用模型还得到了火炮射击周期与系统阻尼比和系统固有频率之间的匹配关系最后给出连发射击时稳定射击时刻的计算     

食饵带疾病的捕食模型的全局稳定性

本文研究了一类三维生态传染病模型的正解性和边界性,并分析了系统平衡点的局部稳定性。利用一种新的几何方法,获得了内平衡点的全稳定性,推广了Li和Muldowney[1]提出的这种方法的应用,这种方法避免了寻找Lyapunov的困难。     

GLOBAL DYNAMICS OF A PREDATOR-PREY MODEL WITH PREY REFUGE AND DISEASE

In this paper, we study a predator-prey model with prey refuge and disease. We study the local asymptotic stability of the equilibriums of the system. Further, we show that the equilibria are globally asymptotically stable if the equilibria are locally asymptotically stable. Some examples are presented to verify our main results. Finally, we give a brief discussion.     

大偏差控制在部分信息下最优投资问题中的应用

利用大偏差控制技术推广部分信息情形下最优投资模型,研究投资者最大化财富增长率超过给定指标的概率.考虑带有红利的股票市场情形,给出了在部分信息情形下带有红利的最优投资策略和最优值函数.     

OPTIMAL CONTROL PROBLEM FOR A PERIODIC PREDATOR-PREY MODEL WITH AGE-DEPENDENCE

In this paper,we investigate optimal policy for periodic predator-prey system with age-dependence.Namely,we consider the model with periodic vital rates and initial distribution.The existence of optimal control strategy is discussed by Mazur's theorem and optimality condition is derived by means of normal cone.     

具有扩散病毒感染群体动力学模型的稳定性与Hopf分歧

讨论了一个具有诺依曼边界条件扩散病毒感染群体动力学模型.证明了模型正常数平衡点的稳定性和扩散引起的Hopf分歧的存在性.     

STABILITY ANALYSIS OF A TRITROPHIC FOOD CHAIN MODEL WITH AN ADAPTIVE PARAMETER FOR THE PREDATOR

Abstract The study of three‐species communities have become the focus of considerable attention, and because the studies of ecological communities start with their food web, we consider a tritrophic food chain model comprised of the prey, the predator, and the super‐predator. The classical assumption of the domino effect is supplemented with an adaptive parameter for the predator (in the absence of prey). Thus, the model exhibits an equilibrium with the predator‐top‐predator steady state, which is a saddle point. Dynamical behaviors such as boundedness, existence of periodic orbits, persistence, as well as stability are analyzed. The long‐term coexistence of the three interacting species is addressed, and the stability analysis of the model shows that the biologically most relevant equilibrium point is globally asymptotically stable whenever it satisfies a certain criterion. Practical implications are explored and related to real populations.     

具有垂直传染和接触传染的传染病模型的稳定性研究

本文研究了一类具有垂直传染和接触传染的传染病模型.利用常微分方程定性与稳定性方法,分析了该模型非负平衡点的存在性及其局部稳定性.同时,利用LaSalle不变性原理和通过构造适当的Lyapunov函数,获得了平凡平衡点、无病平衡点和地方病平衡点全局渐近稳定的充分条件.结果表明当基本再生数小于等于1时,所有种群趋于灭绝;当基本再生数大于1和病毒主导再生数小于1时,病毒很快被清除;当基本再生数大于1和病毒主导再生数大于1以及满足一定条件时,病毒持续流行并将成为一种地方病.     

具有励磁控制的电力系统的稳定性和分岔分析

本文根据[1]所提供的带有励磁控制的发电机电力系统,对该系统的平衡点的局部稳定性和分岔进行了定性分析,当0Vs2(Xd-X'd)/2XdΣ'XdΣ且控制量uf>Efdsc ufc-Efds时,系统存在两类平衡点,其中一类是不稳定的平衡点,而另一类总是稳定的平衡点.Efds uf=Efdsc ufc是鞍结点分岔值,相应于电力系统崩溃.当Efds uf相似文献