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针对病毒变异前和变异后传染病患者具有不同的传染率情形,建立了一类分阶段传播的SIS模型,通过构造Liapunov函数和定性分析,得到病毒变异前和变异后传染病患者平衡点的存在条件以及它们的全局渐近稳定性。 相似文献
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一类具有垂直传染的SIR传染病模型 总被引:4,自引:3,他引:1
讨论了一类具有垂直传染的SIR传染病模型:(dS)/(dt)=6(1-m)(S R) (1- m)pb′I-βSI,(dI)/(dt)=βSI qb′I-d′I-rI,(dR)/(dt)=rI mb(S R) mpb′I-dR获得了无病平衡点与地方病平衡点的全局稳定性. 相似文献
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一类具有常数迁入且总入口在变化的SIRI传染病模型的稳定性 总被引:3,自引:0,他引:3
讨论一类具有常数迁入率,染病类有病死且有效接触率依赖于总人数的SIRI传染病模型.给出了基本再生数σ的表达式.如果σ≤1,则疾病消除平衡点是全局稳定的;如果σ>1,则存在唯一的传染病平衡点且是局部渐近稳定的.对具有双线性传染率和标准传染率的相应模型,进一步证明了当σ>1时传染病平衡点的全局稳定性. 相似文献
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研究了一类潜伏期和感染期均有传染力的SEIQR模型,借助于轨道稳定性,Jacobian矩阵等方法,得到了疾病消亡的阈值——基本再生数R_0,通过构造Lyapunov函数,证明了无病平衡点及地方病平衡点的存在性及全局稳定性. 相似文献
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一类饲养业中发生的传染病模型的全局分析 总被引:1,自引:0,他引:1
根据当所饲养的禽畜发生传染病时饲养业者的实际行为,研究了具有常数输入且输入者中必含潜伏期者的SEQ(I)S模型.利用三维竞争系统的Poincare-Bendixson性质排除了周期解的存在,证明了唯一的疾病存在平衡点的全局稳定性. 相似文献
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一类具有饱和发生率的SEIS模型的全局稳定性 总被引:1,自引:0,他引:1
建立并分析了一类具有饱和发生率、在潜伏期具有传染性的SEIS模型.得到了模型的基本再生数R_0和无病平衡点与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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几个具有隔离项的传染病模型的局部稳定性和全局稳定性 总被引:9,自引:0,他引:9
首先建立了一类具常恢复率,有效接触率依赖于总人数的SIQS传染病模型,并得到了阈值参数σ的表达式.如果σ≤1,则疾病消除平衡点全局稳定;如果σ>1,则存在唯一的传染病平衡点且是局部渐近稳定的。对于带有双线性传染率和标准传染率的两个相应模型,我们进一步证明了当σ>1时传染病平衡点的全局稳定性。其次对于带隔离项修正的传染率的相应模型,我们同样证明了传染病平衡点只要存在唯一就一定全局稳定的结论。上述结果均推广和改进了Hethcote et al.(2002)的相应工作。 相似文献
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考虑了垂直传染和预防接种因素对传染病流行影响的SEIRS模型,主要研究了系统的平衡点及其稳定性,得出当预防接种水平超过某一个阈值时疾病可以根除,若接种水平低于阈值时疾病将流行. 相似文献
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Analysis of an SEIRS epidemic model with two delays 总被引:29,自引:0,他引:29
A disease transmission model of SEIRS type with exponential demographic structure is formulated. All newborns are assumed
susceptible, there is a natural death rate constant, and an excess death rate constant for infective individuals. Latent and
immune periods are assumed to be constants, and the force of infection is assumed to be of the standard form, namely proportional
to I(t)/N(t) where N(t) is the total (variable) population size and I(t) is the size of the infective population. The model consists of a set of integro-differential equations. Stability of the
disease free proportion equilibrium, and existence, uniqueness, and stability of an endemic proportion equilibrium, are investigated.
The stability results are stated in terms of a key threshold parameter. More detailed analyses are given for two cases, the
SEIS model (with no immune period), and the SIRS model (with no latent period). Several threshold parameters quantify the
two ways that the disease can be controlled, by forcing the number or the proportion of infectives to zero.
Received 8 May 1995; received in revised form 7 November 1995 相似文献
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Global stability of an SEIS epidemic model with recruitment and a varying total population size 总被引:11,自引:0,他引:11
This paper considers an SEIS epidemic model that incorporates constant recruitment, disease-caused death and disease latency. The incidence term is of the bilinear mass-action form. It is shown that the global dynamics is completely determined by the basic reproduction number R(0). If R(0)1, a unique endemic equilibrium is globally stable in the interior of the feasible region and the disease persists at the endemic equilibrium. 相似文献
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利用分析技巧研究了一类SEIRS传染病模型的动力学行为.结论表明如果再生数小于1,则带变时滞的传染病模型的无病平衡点是全局指数渐近稳定的,如果再生数大于1,得到传染病平衡点局部指数稳定的充分条件,同时给出了例子说明结论的有效性. 相似文献
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Michael Y. Li John R. Graef Liancheng Wang Jnos Karsai 《Mathematical biosciences》1999,160(2):2640-213
A SEIR model for the transmission of an infectious disease that spreads in a population through direct contact of the hosts is studied. The force of infection is of proportionate mixing type. A threshold sigma is identified which determines the outcome of the disease; if sigma < or = 1, the infected fraction of the population disappears so the disease dies out, while of sigma > 1, the infected fraction persists and a unique endemic equilibrium state is shown, under a mild restriction on the parameters, to be globally asymptotically stable in the interior of the feasible region. Two other threshold parameters sigma' and sigma are also identified; they determine the dynamics of the population sizes in the cases when the disease dies out and when it is endemic, respectively. 相似文献
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本文用Liapunov泛函方法研究捕食者有无限时滞效应的捕食-被捕食系统的平衡状态的稳定性.文章提供了判定系统的平衡状态全局渐近稳定的简单条件,不要求积分核指数衰减. 相似文献