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研究了一类SEIS传染病模型的全局稳定性,通过构造Liapunov泛函,证明了当潜伏期较小,染病期较长并且再生数接近于1时,该模型的地方病平衡点是全局渐近稳定的。 相似文献
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本文建立了一个吸毒人群具有吸毒年龄,治疗人群具有治疗年龄的海洛因传播模型.得到了基本再生数.通过波动引理和李雅普诺夫泛函,证明了当基本再生数小于1时无海洛因吸食平衡点是全局渐近稳定的,当基本再生数大于1时,海洛因传播平衡点是全局渐近稳定的. 相似文献
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本文研究了在有界区域上带有Neumann边界条件的反应扩散三物种食饵-捕食时滞系统.利用特征值方法和Lyapunov函数找到了该系统平衡点稳定的充分条件,该条件说明时滞限制了稳定性.稳定性中的主要一个结论是当食饵和捕食者间的种内竞争大于种间竞争时正平衡点是全局渐近稳定的.进一步,通过构建上下解证明了当波速相对大时该系统具有连接零平衡点和正平衡点的行波解. 相似文献
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本文研究一个具有时滞,一般接触率,常数出生和疾病引起死亡的流行病模型.假设时滞表示暂时免疫期,即恢复者再次变成易感者所需要的时间,同时在模型中考虑了对易感者和恢复者的接种.本文得到了基本再生数R0.分析了模型的无病平衡点和地方病平衡点的存在性.通过Hurwitz准则,研究了无病平衡点和地方病平衡点的局部渐近稳定性.通过Liapunov泛函和Lasalle不变原理,证明了无病平衡点的全局渐近稳定性及在双线性接触率的情况下地方病平衡点的全局渐近稳定性.研究结果表明:R0与对易感者的有效接种率P有关,并且通过增加接种率P可以根除疾病.最后给出了数值模拟. 相似文献
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本文主要研究了具有三个年龄阶段的离散SCIRS模型的动力学性态.首先,利用再生矩阵的方法定义了模型的基本再生数R0,证明了当R01时,模型存在唯一的无病平衡点并且是全局渐近稳定的,当R01时,除了无病平衡点,模型还存在唯一的地方病平衡点.其次,利用法定传染病报告的流脑数据,把模型应用到我国流脑的流行传播中.针对模型中很多参数的不确定性,对基本再生数中的参数进行了敏感性分析.最后,在模型的基础上考虑流脑发病的季节因素对模型加以改进,预测分析了我国流脑的发病情况,数值模拟的结果显示季节因素对疾病进展率的影响程度大于对疾病传染率的影响,为控制流脑在我国的流行传播提供建议. 相似文献
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:研究一类具有一般形式非线性饱和传染率染病年龄结构SIS流行病传播数学模型动力学性态,得到疾病绝灭和持续生存的阈值条件——基本再生数。当基本再生数小于或等于1时,仅存在无病平衡点,且在其小于1的情况下,无病平衡点全局渐遗稳定,疾病将逐渐消除;当基本再生数大于1时,存在不稳定的无病平衡点和唯一的局部渐近稳定的地方病平衡点,疾病将持续存在。已有的两类模型可视为本模型的特例,其相关结论可作为本文的推论。 相似文献
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Coalescent theory provides a mathematical framework for quantitatively interpreting gene genealogies. With the increased availability of molecular sequence data, disease ecologists now regularly apply this body of theory to viral phylogenies, most commonly in attempts to reconstruct demographic histories of infected individuals and to estimate parameters such as the basic reproduction number. However, with few exceptions, the mathematical expressions at the core of coalescent theory have not been explicitly linked to the structure of epidemiological models, which are commonly used to mathematically describe the transmission dynamics of a pathogen. Here, we aim to make progress towards establishing this link by presenting a general approach for deriving a model''s rate of coalescence under the assumption that the disease dynamics are at their endemic equilibrium. We apply this approach to four common families of epidemiological models: standard susceptible-infected-susceptible/susceptible-infected-recovered/susceptible-infected-recovered-susceptible models, models with individual heterogeneity in infectivity, models with an exposed but not yet infectious class and models with variable distributions of the infectious period. These results improve our understanding of how epidemiological processes shape viral genealogies, as well as how these processes affect levels of viral diversity and rates of genetic drift. Finally, we discuss how a subset of these coalescent rate expressions can be used for phylodynamic inference in non-equilibrium settings. For the ones that are limited to equilibrium conditions, we also discuss why this is the case. These results, therefore, point towards necessary future work while providing intuition on how epidemiological characteristics of the infection process impact gene genealogies. 相似文献
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Face masks do not completely prevent transmission of respiratory infections, but masked individuals are likely to inhale fewer infectious particles. If smaller infectious doses tend to yield milder infections, yet ultimately induce similar levels of immunity, then masking could reduce the prevalence of severe disease even if the total number of infections is unaffected. It has been suggested that this effect of masking is analogous to the pre-vaccination practice of variolation for smallpox, whereby susceptible individuals were intentionally infected with small doses of live virus (and often acquired immunity without severe disease). We present a simple epidemiological model in which mask-induced variolation causes milder infections, potentially with lower transmission rate and/or different duration. We derive relationships between the effectiveness of mask-induced variolation and important epidemiological metrics (the basic reproduction number and initial epidemic growth rate, and the peak prevalence, attack rate and equilibrium prevalence of severe infections). We illustrate our results using parameter estimates for the original SARS-CoV-2 wild-type virus, as well as the Alpha, Delta and Omicron variants. Our results suggest that if variolation is a genuine side-effect of masking, then the importance of face masks as a tool for reducing healthcare burdens from COVID-19 may be under-appreciated. 相似文献
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考虑到年龄在一些传染病流行过程中的重要影响,建立了一个具有一般传染率的 SIRS 年龄结构仓室模型。通过将模型改写为抽象柯西问题并利用 Hille-Yosida 算子相关定理,分析了模型的动力学性态,讨论了平衡点的稳定性以及平衡点失稳时产生 Hopf 分支的条件。结果表明,当基本再生数小于 1 时,免疫年龄不影响无病平衡点的全局稳定性;当基本再生数大于 1 时,免疫年龄扰动导致地方病平衡点的稳定性改变,从而产生 Hopf 分支。同时,数值模拟验证了理论结果并显示了免疫年龄对模型动力学性态的影响。 相似文献
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In solving problems of geometrically nonlinear structural mechanics, a prominent role is played by formulation of rate equilibrium conditions. In the computational machinery, the evaluation of the stiffness operator provides the trial incremental displacement field as fixed point of an iterative algorithm. The issue is investigated by a new geometric approach to continuum mechanics. Kinematics is described by the motion along a trajectory manifold embedded in the affine four-dimensional space-time. Variational conditions of equilibrium and rate equilibrium are formulated in terms of natural time rates of stress and stretching. The rate elastostatic problem is formulated in the full nonlinear context by adopting a newly contributed rate-elastic constitutive model. The geometric stiffness and forcing operators are expressed in terms of an arbitrary linear spatial connection. It is shown that the adoption of a Levi- Civita connection provides a linear expression of the geometric stiffness involving a curvature term. For bodies in motion in the flat Euclid space with parallel transport by translation, a symmetric expression of the geometric stiffness is obtained, thus extending the standard formula to bodies of any dimensionality. 相似文献
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Utility of R0 as a predictor of disease invasion in structured populations 总被引:1,自引:0,他引:1
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Paul C Cross Philip L.F Johnson James O Lloyd-Smith Wayne M Getz 《Journal of the Royal Society Interface》2007,4(13):315-324
Early theoretical work on disease invasion typically assumed large and well-mixed host populations. Many human and wildlife systems, however, have small groups with limited movement among groups. In these situations, the basic reproductive number, R0, is likely to be a poor predictor of a disease pandemic because it typically does not account for group structure and movement of individuals among groups. We extend recent work by combining the movement of hosts, transmission within groups, recovery from infection and the recruitment of new susceptibles into a stochastic model of disease in a host metapopulation. We focus on how recruitment of susceptibles affects disease invasion and how population structure can affect the frequency of superspreading events (SSEs). We show that the frequency of SSEs may decrease with the reduced movement and the group sizes due to the limited number of susceptible individuals available. Classification tree analysis of the model results illustrates the hierarchical nature of disease invasion in host metapopulations. First, the pathogen must effectively transmit within a group (R0>1), and then the pathogen must persist within a group long enough to allow for movement among the groups. Therefore, the factors affecting disease persistence--such as infectious period, group size and recruitment of new susceptibles--are as important as the local transmission rates in predicting the spread of pathogens across a metapopulation. 相似文献
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This study proposes a modified human immunodeficiency virus (HIV) infection differential equation model with a saturated infection rate. This model has an infection‐free equilibrium point and an endemic infection equilibrium point. Using Lyapunov functions and LaSalle’s invariance principle shows that if the model’s basic reproductive number R 0 < 1, the infection‐free equilibrium point is globally asymptotically stable, otherwise the endemic infection equilibrium point is globally asymptotically stable. It is shown that a forward bifurcation will occur when R 0 = 1. The basic reproductive number R 0 of the modified model is independent of plasma total CD4+ T cell counts and thus the modified model is more reasonable than the original model proposed by Buonomo and Vargas‐De‐León. Based on the clinical data from HIV drug resistance database of Stanford University, using the proposed model simulates the dynamics of two group patients’ anti‐HIV infection treatments. The simulation results have shown that the first 4 weeks’ treatments made the two group patients’ R′ 0 < 1, respectively. After the period, drug resistance made the two group patients’ R′ 0 > 1. The results explain why the two group patients’ mean CD4+ T cell counts raised and mean HIV RNA levels declined in the first period, but contrary in the following weeks.Inspec keywords: microorganisms, cellular biophysics, differential equations, Lyapunov methods, blood, drugs, patient treatment, RNAOther keywords: global stability, infection‐free state, endemic infection state, modified human immunodeficiency virus infection model, HIV, differential equation model, saturated infection rate, infection‐free equilibrium point, endemic infection equilibrium point, Lyapunov functions, LaSalle invariance principle, forward bifurcation, plasma total CD4+ T cell counts, HIV drug resistance database, mean HIV RNA levels 相似文献