周期演化域上一个禽流感模型的动力学分析

本文研究了周期演化区域上一个禽流感模型.首先假设区域的增长为各向同性,将模型转换为固定区域上的反应扩散问题.然后利用相关的特征值问题和上下解方法得出模型解的渐近性态.研究结果表明,周期性区域的演化对疾病的传播与抑制取决于区域的周期演化速率ρ(t)的积分平均值ρ-2=1/T∫0T1/ρ2(t)dt.若ρ-2>1,则周期性区域的演化可抑制疾病的传播;若ρ-2<1,则周期性区域的演化可加速疾病的传播;若ρ-2=1,则周期性区域的演化对疾病的传播没有影响.     

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.     

公共教育影响的SIR传染病斑块模型性态分析

建立了考虑公共卫生教育影响的SIR斑块模型.通过分析模型动力学性态,给出模型平衡点存在条件,并证明了无病平衡点和地方病平衡点的稳定性.通过数值模拟分析公共卫生教育和斑块间的传播对模型疾病传播的影响,发现媒体的传播和公众之间的交流可以促进疾病防护意识,进而降低传染及传播疾病的几率.当疾病爆发时,应尽量减少人口流通,当疾病爆发后,应加强疾病防护意识的传播,尤其是医疗水平较低的地区.     

第七届北京高中数学知识应用竞赛初赛试题

1.可以使用任何参考资料和计算工具. 2.考试形式为开卷,时间从12月12日16:00开始,12月15日8:00准时交卷. 一、(满分16分)SARS(Severe Acute Respiratory Syndrome),严重急性呼吸综合症,俗称(非典型肺炎)是21世纪第一个在世界范围内传播的疾病.今年春天在我国多处爆发和蔓延,给     

复杂网络疾病传播动力学研究进展

复杂网络有自身的动力学性质,这可以通过定义相应的拓扑统计量来刻画;另一方面,网络的拓扑结构对其上的动力学过程,尤其是疾病传播过程,具有重要影响.本文简要回顾了复杂网络理论发展的几个重要标志及一些经典的疾病传播动力学模型,重点介绍了退火网络、淬火网络、自适应网络和耦合网络上疾病传播的相关研究成果以及网络疾病建模思想在其它一些社会传播中的应用.最后,根据作者本人的工作和理解,提出了一些值得进一步思考和研究的问题.     

应用传染病模型估计校园急性出血性结膜炎暴发的最终规模

个体差异性会导致疾病传播的时空异质性,人群卫生习惯差异性影响着疾病传播的基本再生数与最终规模.以2011年长沙市某校急性出血性结膜炎(AHC)暴发疫情为例,将人群分为卫生习惯较好(N_1)与卫生习惯较差(N_2)两组,运用分组动力学模型评估急性出血性结膜炎暴发疫情中的基本再生数与最终规模.研究发现,基本再生数与最终规模随着N_1比例的增大而减小;较好卫生习惯人群中以δ比例降低了传染性.当两组人数比例为10:1δ=0.1时,最终规模降低了84%;而当δ0.5时,此时已经没有明显变化.     

一类具有直接和间接传播的SIV传染病模型

传染病的传播途径是多种多样的,如:直接传播和间接传播等.在以往的传染病模型中,大多是只考虑直接传播对疾病的影响,而忽略了环境作用对疾病的影响,即间接传播的影响.其实,间接传播在传染病的传播中同样起着重要的作用,忽略间接传播的影响会低估基本再生数,从而错估传染病爆发的规模,给人类的健康带来更大的威胁.研究了一个既有直接传播又有间接传播的SⅣ传染病模型,通过研究模型的动力学行为,给出了无病平衡点和地方病平衡点全局渐近稳定的条件,并用数值模拟证实了该结果.     

一类带有感染年龄SIR模型最优化免疫策略的存在性

对于一个免疫策略来讲,付出(单位时间内接种疫苗的数量)和效果(再生数的大小)是两个重要概念.在给定的费用下找到带有最小再生数的策略和在给定的再生数下找到最小费用的策略是两个最优问题.对一个确定的免疫策略来说,人群中的易感群体和染病群体会趋于相对稳定的状态.当一种疾病侵袭已免疫人群时,用带有感染年龄的SIR模型去描述这类疾病的传播更为准确.因此,本文研究了一类带有感染年龄的SIR模型,得到了最优化策略的存在性.     

女性吸毒者在HIV/AIDS传播中的作用

利用数学模型,探讨了女性吸毒者在HIV/AIDS传播中的作用.通过理论分析和数值模拟,揭示了女性吸毒者对HIV/AIDS传播和流行的重要作用:当HIV/AIDS在吸毒人群和一般男性人群中流行时,若切断女性吸毒人群和一般男性人群间的传播途径(商业性行为),则疾病不但在一般男性人群中会消亡,在一定的条件下,甚至会在吸毒人群中消亡.     

一类具有一般出生函数阶段结构的传染病模型的全局分析

假设种群个体生长分幼年和成年两个阶段以及疾病仅在成年阶段传播,建立并研究了一类幼年个体输入率为一般函数的传染病模型,得到了决定种群存活与否的种群存活基本再生数和决定疾病传播灭绝与否的疾病传播基本再生数,通过构造适当的Lyapunov函数分析了模型的全局阈值动力学性态.     

Discreteness of the exterior transmission eigenvalues

In this paper we consider a kind of exterior transmission problem in which the refractive index n(x) is a piecewise positive constant. Through establishing an equivalent boundary integral system, we obtain that the set of exterior transmission eigenvalues is a discrete set. Furthermore, we prove that there does not exist a transmission eigenvalue under some conditions.     

Uniform estimates for transmission problems with high contrast in heat conduction and electromagnetism

In this paper we prove uniform a priori estimates for transmission problems with constant coefficients on two subdomains, with a special emphasis for the case when the ratio between these coefficients is large. In the most part of the work, the interface between the two subdomains is supposed to be Lipschitz. We first study a scalar transmission problem which is handled through a converging asymptotic series. Then we derive uniform a priori estimates for Maxwell transmission problem set on a domain made up of a dielectric and a highly conducting material. The technique is based on an appropriate decomposition of the electric field, whose gradient part is estimated thanks to the first part. As an application, we develop an argument for the convergence of an asymptotic expansion as the conductivity tends to infinity.     

An uniqueness result with some density theorems with interior transmission eigenvalues

Given a set of transmission eigenvalues, we apply Cartwright’s theory to show the density function inversely determines the indicator function. This indicator function gives a Weyl’s type of asymptotics on the transmission eigenvalues. The inverse uniqueness problem on the refraction index is reduced to identifying a parameter of an entire function. We use a Carlson’s type of theorem to prove the uniqueness as in entire function theory. Taking advantage of the uniqueness of rod density problem, we prove an uniqueness result with interior transmission eigenvalues.     

具有无穷多个不连续点Sturm-Liouville算子的Friedrichs扩张

研究了一类内部具有无穷多个不连续点的Sturm-Liouville问题,即内部具有无穷多个转移条件的Sturm-Liouville问题.把此类问题放到一个新的空间中去考虑,定义了与转移条件相关联的最小算子Cmin和最大算子Cmax,给出了最小算子Cmin是下有界的一个充分条件,进一步由边界条件刻画了具有下有界的最小算子Cmin的Friedrichs扩张.     

On 2-Connected Transmission Irregular Graphs

The transmission of a vertex v in a graph is the sum of the distances from v to all other vertices of the graph. In a transmission irregular graph, the transmissions of all vertices are pairwise distinct. It is known that almost all graphs are not transmission irregular. Some infinite family of transmission irregular trees was constructed by Alizadeh and Klav?ar [Appl.Math. Comput. 328, 113–118 (2018)] and the following problemwas formulated: Is there an infinite family of 2-connected graphs with the property? In this article, we construct an infinite family of 2-connected transmission irregular graphs.     

On the solvability of a transmission problem for the Laplace operator with a dynamic boundary condition on a nonregular interface

In this paper, we consider a transmission problem for the Laplace operator when an interface contains angular points and time derivatives of the unknown functions enter in the transmission condition. We prove the existence of a unique solution in the weighted Hölder classes.     

“Magic” Dispersion Maps with Distributed Raman Amplification

We analyze pulse propagation in an optical fiber with a periodic dispersion map and distributed amplification. Using an asymptotic theory and a momentum method, we identify a family of dispersion management schemes that are advantageous for massive multichannel soliton transmission. For the case of two-step dispersion maps with distributed Raman amplification to compensate for the fiber loss, we find special schemes that have optimal (chirp-free) launch point locations that are independent of the fiber dispersion. Despite the variation of dispersion with wavelength due to the fiber dispersion slope, the transmission in several different channels can be optimized simultaneously using the same optimal launch point. The theoretical predictions are verified by direct numerical simulations. The obtained results are applied to a practical multichannel transmission system.     

A Joint DAE/PDE Model for Interconnected Electrical Networks

To model transmission lines effects in integrated circuits, we couple the network equations for the circuits with the telegrapher's equations for the transmission lines. This results in an initial/boundary value problem for a mixed system of Differential-Algebraic Equations (DAEs) and hyperbolic Partial Differential Equations (PDEs). By semidiscretization the system is transformed into differential-algebraic equations in time only. We apply this modeling approach to a CMOS ring oscillator, an oscillatory circuit with transmission lines as coupling units, and discuss the simulation results.     

Fully nonlinear elliptic equations and the dini condition

Abstract

We investigate transmission problems with strongly Lipschitz interfaces for the Dirac equation by establishing spectral estimates on an associated boundary singular integral operator, the rotation operator. Using Rellich estimates we obtain angular spectral estimates on both the essential and full spectrum for general bi-oblique transmission problems. Specializing to the normal transmission problem, we investigate transmission problems for Maxwell's equations using a nilpotent exterior/interior derivativeoperator. The fundamental commutation properties for this operator with the two basic reflection operators are proved. We show how the L ₂spectral estimates are inherited for the domain of the exterior/interior derivative operator and prove some complementary eigenvalue estimates. Finally we use a general algebraic theorem to prove a regularity property needed for Maxwell's equations.     

Transmission eigenvalue problem for inhomogeneous absorbing media with mixed boundary condition

Consider the transmission eigenvalue problem for the wave scattering by a dielectric inhomogeneous absorbing obstacle lying on a perfect conducting surface. After excluding the purely imaginary transmission eigenvalues, we prove that the transmission eigenvalues exist and form a discrete set for inhomogeneous non-absorbing media, by using analytic Fredholm theory. Moreover, we derive the Faber-Krahn type inequalities revealing the lower bounds on real transmission eigenvalues in terms of the media parameters. Then, for inhomogeneous media with small absorption, we prove that the transmission eigenvalues also exist and form a discrete set by using perturbation theory. Finally, for homogeneous media, we present possible components of the eigenvalue-free zone quantitatively, giving the geometric understanding on this problem.