两类带有确定潜伏期的SEIS传染病模型的分析

通过研究两类带有确定潜伏期的SEIS传染病模型,发现对种群的常数输入和指数输入会使疾病的传播过程产生本质的差异．对于带有常数输入的情形,找到了地方病平衡点存在及局部渐近稳定的阈值,证明了地方病平衡点存在时一定局部渐近稳定,并且疾病一致持续存在．对于带有指数输入的情形,发现地方病平衡点当潜伏期充分小时是局部渐近稳定的,当潜伏期充分大时是不稳定的．     

一类潜伏期有传染性的传染病模型动力学分析

建立了一类潜伏期具备传染性的传染病传播模型,根据疾病传播规律求解了疾病消失和持续生存的阈值——基本再生数.对系统的稳定性进行了讨论,得到了系统稳定性条件.最后,以COVID-19为例,解释了各种举措在疾病控制中的作用,并对疫情传播扩散做了探讨和预测.     

带有脉冲免疫和传染年龄的SIV传染病模型解的存在性

我们建立带有脉冲免疫和传染年龄的SIV传染病模型,这类传染病在潜伏期具有传染性,总人口规模依赖时间,并且传染类的康复率和传染年龄有关.我们证明此类模型解存在唯一.     

新型冠状病毒肺炎疫情控制策略研究:效率评估及建议

基于传播动力学及普适SEIR (susceptible-exposed-infectious-recovered/removed)模型和程序Epi SIX (模型总参数只有10个),实时跟踪国家及各地卫生健康委员会(简称卫健委)自2019年12月12日以来发布的确诊数据,对新型冠状病毒肺炎(简称新冠肺炎)疫情的流行趋势进行了研判,对疾控策略的效率进行了评估,并将相应的建议提供给疾控方参考.特别地,厘清了这次疫情的流行病学基本参数,如基本再生数、平均潜伏期、平均传染期、非典型患者占比和流行趋势,包括流行时间、疫情拐点、流行规模,并分析了控制强度对传播的影响等.同时创建了一个网页来更新预测结果.     

一类S_nIR流行病模型的全局稳定性

根据易感类个体对病毒的易感性不同把传统的易感类S分成n个子类Sk(k=1,2,…,n),建立了SnIR流行病的数学模型,通过对平凡平衡点局部稳定性的分析得到了基本再生数的数学表达式,利用Liapunnov稳定性理论研究了平衡点的稳定性,得到了平凡平衡点全局稳定性及非平凡平衡点全局稳定性的阈值条件.     

具有时滞和阶段结构的生态-流行病模型的稳定性及其Hopf分支

本文研究一个食饵具有阶段结构和捕食者染病的捕食者-食饵模型的稳定性,并讨论了由疾病的潜伏期引起的时滞对种群动力学性态的影响.通过分析特征方程,运用Hurwitz判定定理,讨论了该模型的平凡平衡点、捕食者灭绝平衡点、无病平衡点及地方病平衡点的局部稳定性,并得到了地方病平衡点附近Hopf分支存在的充分条件;通过构造适当的Lyapunov泛函,运用La Sall不变集原理,得到了这些平衡点全局稳定的充分条件.     

带信息干预和带饱和感染率的随机SIRS模型流行病的灭绝性

讨论了一类带信息干预和饱和感染率的随机SIRS模型的动力学行为.通过构造合适的Lyapunov函数,证明了随机模型全局正解的存在唯一性.运用鞅的强大数定律、微分方程比较定理等随机分析理论,得到了疾病灭绝的充分条件.最后,通过数值例子验证了理论结果的正确性,并运用数值模拟研究了信息干预的强度对流行病的影响.     

一类潜伏期与传染期均传染的SEIQR传染病模型

研究了一类潜伏期和感染期均传染的SEIQR模型的全局稳定性,找到疾病绝灭和持续生存的阈值——基本再生数R0,证明了无病平衡点和地方病平衡点的存在性和全局渐近稳定性,揭示了隔离对疾病控制的积极作用。     

潜伏期和染病期均具有康复的年龄结构MSEIS流行病模型的稳定性

本文建立和研究了潜伏期和染病期均具有康复的年龄结构MSEIS流行病模型.在总人口规模不变的假设下,得到了决定疾病消亡与否的基本再生数R0的表达式,证明了当R0＜1时,无病平衡点是局部和全局渐近稳定的,此时疾病消失;当R0＞1时,无病平衡点不稳定,此时系统至少存在一个地方病平衡点,并在一定条件下证明了地方病平衡点的局部渐近稳定性.     

具有非单调发病率的随机SIS模型的持续性与灭绝性

讨论了一类具有非单调发病率的随机SIS模型.主要贡献在两个方面.在数学上,应用随机分析技术证明了R_0~s可以作为随机模型的阈值.当R_0~s1时,随机模型存在一个无病的吸引集,即疾病会以概率1灭绝.当R_0~s1时,疾病是随机持续生存的.在流行病学上,结果表明环境噪声可以抑制疾病的爆发,可以为疾病的预防和控制提供一些参考.     

Influence of temporal aggregation on strategic forest management under risk of wind damage

A key aspect when optimizing strategic and long-term forest management policies is the temporal aggregation utilizing time periods of a specific length. As the length of the time periods influence both the problem size and the possible interaction of the management policy with the state of the forest, it implicitly has a major influence on the feasibility of computing the optimal management policy and the quality of the resulting management policy. The objective of this study was twofold: (i) to evaluate the value of considering the risk of wind damage in large-scale strategic forestry management policies, (ii) to investigate the influence of the length of the time periods on the value of considering the risk of wind damage in the management policy. The analysis was executed utilizing a graph-based Markov decision process model capable of considering stochastic wind damage event, and a case study utilizing a forest estate consisting of 1200 ha of forestry, divided into 623 stands. Twenty-, ten-, and five-year-long time periods were utilized to evaluate the influence of the length of the time periods, while the value of considering the risk of wind damage in the management of the estate was evaluated by optimizing and evaluating long-term management policies recognizing and not recognizing the risk of wind damage. Results show that the value of considering the risk of wind damage was small for the whole estate. The expected net present value of the estate increased by ≤2% by managing the estate according to the risk of wind damage. Furthermore, while the length of the time periods had a small influence on the scale of the entire estate, it had a larger influence on the scale of a smaller subset of stands in the estate. For the whole estate, the value of considering the risk of wind damage varied with ≤1.5% depending on the length of the time periods. While for a selected subset of stands, the value of considering the risk of wind damage varied with ≤6.5% depending on the length of the time periods.     

Standard passivity-based control for multi-hydro-turbine governing systems with surge tank

This paper addresses the problem of control design for hydro-turbine governing systems with surge tanks from the perspective of standard passivity-based control. The dynamic model of a synchronous machine is considered in conjunction with a model of the hydro-turbine to generate an eleventh-order nonlinear set of differential equations. An Euler–Lagrange representati of the system and its open-loop dynamics is developed. Then, the standard passivity-based control is applied to design a global and asymptotically stable controller in closed-loop operation. The proposed control is decentralized to avoid challenges of communication between the hydro-turbine governing systems. The proposed standard passivity-based control approach is compared with two control approaches. First, a classical standard cascade proportional-integral-derivative controller is applied for the governing system, the automatic voltage regulator, and the excitation system. Second, a sliding mode control is also implemented in the governing system. Two test systems were used to validate the performance of the proposed controller. The first test system is a single machine connected to an infinite bus, and the second test system is the well-known Western System Coordinating Council’s multimachine system. Overall, simulation results show that the proposed controller exhibits a better dynamic response with shorter stabilization times and lower peaks during the transient periods.     

A direct method for solving an anisotropic mean curvature flow of plane curves with an external force

A new method for solution of the evolution of plane curves satisfying the geometric equation v=β(x,k,ν), where v is the normal velocity, k and ν are the curvature and tangential angle of a plane curve Γ ? ?² at the point x∈Γ, is proposed. We derive a governing system of partial differential equations for the curvature, tangential angle, local length and position vector of an evolving family of plane curves and prove local in time existence of a classical solution. These equations include a non‐trivial tangential velocity functional governing a uniform redistribution of grid points and thus preventing numerically computed solutions from forming various instabilities. We discretize the governing system of equations in order to find a numerical solution for 2D anisotropic interface motions and image segmentation problems. Copyright © 2004 John Wiley & Sons, Ltd.     

Mixing and charge transfer in a nanofluidic system due to a patterned surface

In this work, electroosmotic flow mixing enhancement is investigated in a sufficiently long nano-channel with a rectangular nonconducting obstacle mounted on the lower wall with heterogeneous surface electrical potential. A linear pressure drop is observed above the region of patch potential to form a recirculating zone. Formation of vortical flow due to the combined effect of enhanced surface area, heterogeneity in surface potential and external electric field is discussed. A numerical method is adopted based on a finite volume approach to solve the governing coupled Nernst–Planck, Navier–Stokes and Maxwell’s equations to describe ion transport, electrical potential distribution and their impact on flow field. It is observed that an increment in patch potential strength and block height increases the species concentration gradient and surface area, respectively, which enhances the diffusive flux resulting in better mixing performance.     

Departure from linear mechanical behaviour of a helical spring

We model small deviations from linear mechanical behaviour of a loaded vertically suspended helical spring. A Taylor expansion of the elasticity equations governing the axial extension of the spring is used to determine the relative magnitudes of linear and (quadratic and cubic) nonlinear terms in the force–extension relationship. This relationship is the basis for the derivation of a model for the static extension of a loaded spring, and a wave equation that models small amplitude oscillation. The models account for the natural decline in pitch angle down a suspended spring, and provide accurate fits to measurements of static extension and periods of oscillation that are not adequately represented by equations based on Hooke’s law. The static and dynamic data yield consistent estimates of the spring rate.     

Surface effects on nonlinear free vibration of functionally graded nanobeams using nonlocal elasticity

In this paper, to consider all surface effects including surface elasticity, surface stress, and surface density, on the nonlinear free vibration analysis of simply-supported functionally graded Euler–Bernoulli nanobeams using nonlocal elasticity theory, the balance conditions between FG nanobeam bulk and its surfaces are considered to be satisfied assuming a cubic variation for the component of the normal stress through the FG nanobeam thickness. The nonlinear governing equation includes the von Kármán geometric nonlinearity and the material properties change continuously through the thickness of the FG nanobeam according to a power-law distribution of the volume fraction of the constituents. The multiple scale method is employed as an analytical solution for the nonlinear governing equation to obtain the nonlinear natural frequencies of FG nanobeams. The effect of the gradient index, the nanobeam length, thickness to length ratio, mode number, amplitude of deflection to radius of gyration ratio and nonlocal parameter on the frequency ratios of FG nanobeams is investigated.     

Nonlife ratemaking and risk management with Bayesian generalized additive models for location,scale, and shape

Generalized additive models for location, scale and, shape define a flexible, semi-parametric class of regression models for analyzing insurance data in which the exponential family assumption for the response is relaxed. This approach allows the actuary to include risk factors not only in the mean but also in other key parameters governing the claiming behavior, like the degree of residual heterogeneity or the no-claim probability. In this broader setting, the Negative Binomial regression with cell-specific heterogeneity and the zero-inflated Poisson regression with cell-specific additional probability mass at zero are applied to model claim frequencies. New models for claim severities that can be applied either per claim or aggregated per year are also presented. Bayesian inference is based on efficient Markov chain Monte Carlo simulation techniques and allows for the simultaneous estimation of linear effects as well as of possible nonlinear effects, spatial variations and interactions between risk factors within the data set. To illustrate the relevance of this approach, a detailed case study is proposed based on the Belgian motor insurance portfolio studied in Denuit and Lang (2004).     

The Passage of Weakly Coupled Nonlinear Oscillators through Internal Resonance

An asymptotic procedure for deriving equations governing the passage of a weakly coupled nonlinear system of oscillators is discussed. The procedure avoids an inner-outer-matching technique and is valid when the small coupling and detuning parameters are arbitrary. Resonance is permitted to occur at one or several instances of time or to last for a finite length of time. Numerical results are discussed.     

New method for deriving equations of an effective average model of periodic media

This new method for deriving the equations of an effective average model involves constructing exact expressions for the displacement and stress fields for the periodic medium. The limit of an infinite number of periods is then taken, wish an infinite decrease in the length of the periods. Equations satisfied by the displacement and stress fields after this limit is taken are found. Since these equations are independent of the source, they are treated as the equations of an effective average model.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 195, pp. 82–102, 1991.     

Size-dependent buckling analysis of functionally graded third-order shear deformable microbeams including thermal environment effect

Presented herein is the prediction of buckling behavior of size-dependent microbeams made of functionally graded materials (FGMs) including thermal environment effect. To this purpose, strain gradient elasticity theory is incorporated into the classical third-order shear deformation beam theory to develop a non-classical beam model which contains three additional internal material length scale parameters to consider the effects of size dependencies. The higher-order governing differential equations are derived on the basis of Hamilton’s principle. Afterward, the size-dependent differential equations and related boundary conditions are discretized along with commonly used end supports by employing generalized differential quadrature (GDQ) method. A parametric study is carried out to demonstrate the influences of the dimensionless length scale parameter, material property gradient index, temperature change, length-to-thickness aspect ratio and end supports on the buckling characteristics of FGM microbeams. It is revealed that temperature change plays more important role in the buckling behavior of FGM microbeams with higher values of dimensionless length scale parameter.