共查询到19条相似文献,搜索用时 109 毫秒
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讨论了具有垂直传染且总人口在变化的连续预防接种SIRS传染病模型,给出了基本再生数R_0的表达式,并利用广义Bendixson-Dulac函数方法证明了无病平衡点和地方病平衡点的全局稳定性. 相似文献
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建立了具有非线性接触率脉冲预防接种的SIR传染病模型,利用脉冲微分方程理论,对模型的动力学性态进行了分析,给出了模型的阀值,证明了无病周期解的存在性及全局渐近稳定性. 相似文献
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一类带有隔离和接种的传染病模型的稳定性分析 总被引:2,自引:0,他引:2
董淑转 《数学的实践与认识》2007,37(20):175-178
建立并分析一类带有隔离和接种传染病模型,证明了系统解的非负性,利用V函数和极限方程理论,证明无病平衡点和地方病平衡点的全局渐近稳定性. 相似文献
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建立并分析了一类具有脉冲预防接种的垂直传染的SIR传染病模型,给出了系统解的一致有界性及无病周期解的存在的充分条件,根据Floquer乘子理论及脉冲微分不等式,证明了无病周期解的局部稳定性及全局渐近稳定性. 相似文献
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本文建立了一类具有病毒变异的Logistic死亡率SEIR传染病模型,借助Lyapunov函数和LaSalle''s不变原理,证明了无病平衡点全局稳定性.利用代数方法构造Lyapunov函数,证明了地方病平衡点全局稳定性.另外,通过数值模拟分析了参数对疾病传播的影响. 相似文献
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一类带有一般接触率和常数输入的流行病模型的全局分析 总被引:12,自引:1,他引:11
借助极限系统理论和构造适当的Liapunov函数,对带有一般接触率和常数输入的SIR型和SIRS型传染病模型进行讨论.当无染病者输入时,地方病平衡点存在的阈值被找到A·D2对相应的SIR模型,关于无病平衡点和地方病平衡点的全局渐近稳定性均得到充要条件;对相应的SIRS模型,得到无病平衡点和地方病平衡点全局渐近稳定的充分条件.当有染病者输入时,模型不存在无病平衡点.对相应的SIR模型,地方病平衡点是全局渐近稳定的;对相应的SIRS模型,得到地方病平衡点全局渐近稳定的充分条件. 相似文献
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通过假设被接种者具有部分免疫,建立了一类具有潜伏期和接种的SEIR传染病模型,借助再生矩阵得到了确定此接种模型动力学行为的基本再生数.当基本再生数小于1时,模型只有无病平衡点;当基本再生数大于1时,除无病平衡点外,模型还有唯一的地方病平衡点.借助Liapunov函数,证明了无病平衡点和地方病平衡点的全局稳定性. 相似文献
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具脉冲预防接种的SIRS传染病模型中地方病周期解的存在性 总被引:1,自引:0,他引:1
对具脉冲预防接种的SIRS传染病模型进行分析,利用分支理论得到了系统中地方病周期解的存在性,并利用数值模拟的方法验证了所得结论的正确性,完善了对该系统的讨论结果 相似文献
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Although impulsive differential equations have become a widely concerned subject and a lot of models with impulsive effect have been studied in recent years, biochemical reaction models with impulsive input are rarely studied. In this paper, we consider an irreversible three molecular reaction model with impulsive input. By using the Floquet theorem and the method for the small parameter of impulsive differential equations, we obtain sufficient conditions for asymptotical stability and global stability of the given system. The existence of a positive periodic solution is also studied by the bifurcation theory. Further, we also show that our given conditions are right by numerical simulations. 相似文献
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具饱和传染率的脉冲免疫接种SIRS模型 总被引:1,自引:0,他引:1
研究了具饱和传染率的脉冲免疫接种SIRS模型的一致持续生存和周期解,得到了无病周期解全局渐近稳定的充分条件和系统一致持续生存的充分条件,并应用分支理论得到了正周期解存在的分支参数. 相似文献
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In this paper, we formulate and investigate the pest control models in accordance with the mathematical theory of epidemiology. We assume that the release of infected pests is continuous and impulsive, respectively. Therefore, our models are the ordinary differential equations and the impulsive differential equations. We study the global stability of the equilibria of the ordinary differential equations. The permanence of the impulsive differential equations is proved. By means of numerical simulation, we obtain the critical values of the control variable under different methods of release of infected pests. Thus, we provide a mathematical evidence in the management of an epidemic controlling a pest. 相似文献
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Existence and Approximate Controllability of Solutions for an Impulsive Evolution Equation with Nonlocal Conditions in Banach Space 下载免费PDF全文
Lixin Sheng Weimin Hu You-Hui Su Yongzhen Yun 《Journal of Nonlinear Modeling and Analysis》2024,6(1):194-209
In this article, we study the existence of mild solutions and approximate controllability for non-autonomous impulsive evolution equations with nonlocal conditions in Banach space. The existence of mild solutions and some conditions for approximate controllability of these non-autonomous impulsive evolution equations are given by using the Krasnoselskii''s fixed point theorem, the theory of evolution family and the resolvent operator. In particular,the impulsive functions are supposed to be continuous and the nonlocal item is divided into Lipschitz continuous and completely bounded. An example is given as an application of the results. 相似文献
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Masaki Sekiguchi Emiko Ishiwata 《Journal of Mathematical Analysis and Applications》2010,371(1):195-1008
We derive a discretized SIRS epidemic model with time delay by applying a nonstandard finite difference scheme. Sufficient conditions for the global dynamics of the solution are obtained by improvements in discretization and applying proofs for continuous epidemic models. These conditions for our discretized model are the same as for the original continuous model. 相似文献
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Meihong Qiao Anping Liu Urszula Foryś 《Mathematical Methods in the Applied Sciences》2013,36(6):695-706
Control of epidemic infections is a very urgent issue today. To develop an appropriate strategy for vaccinations and effectively prevent the disease from arising and spreading, we proposed a modified Susceptible‐Infected‐Removed model with impulsive vaccinations. For the model without vaccinations, we proved global stability of one of the steady states depending on the basic reproduction number R0. As typically in the epidemic models, the threshold value of R0 is 1. If R0 is greater than 1, then the positive steady state called endemic equilibrium exists and is globally stable, whereas for smaller values of R0, it does not exist, and the semi‐trivial steady state called disease‐free equilibrium is globally stable. Using impulsive differential equation comparison theorem, we derived sufficient conditions under which the infectious disease described by the considered model disappears ultimately. The analytical results are illustrated by numerical simulations for Hepatitis B virus infection that confirm the theoretical possibility of the infection elimination because of the proper vaccinations policy. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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Yoshiaki Muroya Yoichi Enatsu Toshikazu Kuniya 《Nonlinear Analysis: Real World Applications》2013,14(3):1693-1704
In this paper, by extending well-known Lyapunov function techniques to SIRS epidemic models, we establish sufficient conditions for the global stability of an endemic equilibrium of a multi-group SIRS epidemic model with varying population sizes which has cross patch infection between different groups. Our proof no longer needs such a grouping technique by graph theory commonly used to analyze the multi-group SIR models. 相似文献
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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 总被引:2,自引:0,他引:2
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. 相似文献