一类具有垂直传染与接种的DS—I—R传染病模型研究

本文研究了-类具有垂直传染与接种的疾病在多个易感群体中传播的DS-I-R传染病模型,得到了疾病流行的阈值.运用微分方程定性与稳定性理论分析了无病平衡点的局部稳定与全局渐近稳定性及存在唯一地方病平衡点与其全局渐近稳定性.     

稳定性切换在一阶时滞微分方程中的应用

介绍了时滞动力系统中的对零解稳定性讨论的稳定性切换法,并应用此方法对时滞动力系统中的三个一阶时滞微分方程基本定理给予证明.同时表明了在局部稳定性分析中,该方法有着更大的优势.     

基于媒体报道的Filippov传染病模型的全局动力学

在经典传染病模型的基础上,通过考虑阈值策略,研究了一类基于媒体报道的不连续的传染病模型.利用Filippov意义下的右端不连续微分方程理论,对阈值策略下传染病模型的动力学行为进行了定性分析,并利用Poincaré映射研究了无病平衡点、地方病平衡点及伪平衡点的全局渐近稳定性.     

具比率依赖型HollingⅡ功能反应函数的两种群系统的最优税收策略

研究了具比率依赖型功能性反应函数的两种群系统,利用微分方程定性理论得到了系统正平衡点的存在性、局部渐近稳定性及全局渐近稳定性的条件,并且由Pontryagin最大值原理得到了最优税收策略.     

具斑块迁移的病毒模型的稳定性分析

研究了一类未感染细胞斑在两斑块间迁移的病毒模型.获得了无病平衡点全局稳定性以及地方病平衡点稳定性的充分条件.研究结果表明阈值R <1且感染细胞生成病毒的速度相对小而病毒细胞死亡率足够大时,病毒趋于灭绝;而阈值R> 1且感染细胞生成病毒的速度相对大而病毒细胞死亡率足够小时,病毒持续流行.     

带有积分条件的泛函微分方程的稳定性分析

本文讨论了下列泛函微分方程: 这里T>0,T_1≥0。令Q=bf(a)/c。若Q≤1,则上述方程有唯一平衡点且全局稳定。若Q>1,则上述方程的正平衡点渐近稳定,另一平衡点不稳定。所采用的证明方法是构成Lyapunov泛函和利用广义持征方程,与[2]、[3]不同.当f(y)=y即可得K.L.cooke[3]的结论.当T=T_1=O,f(y)=y即可得[2]的讨论。     

脉冲微分方程的两度量实用稳定性

利用向量Lyapunov函数,研究了脉冲微分方程的两度量实用稳定性问题,通过实例对得到的稳定性的结论给予了验证.     

确定高精度参数问题

在航天器精确制导等高科技的实际问题中,必须高精度地估计模型中的大批参数,建立高精度的数学模型,考虑较简单的确定高精度参数问题:食饵-捕食者系统.对于绝大多数微分方程得不到解析解,尤其是非线性微分方程这样的情况,运用稳定性理论和常微分方程几何理论来分析该生态模型.在数据分析处理中,采用了大量优化算法,如灰色系统辩识方法,多项式曲线选阶及拟合算法,牛顿迭代法等等.最后,通过MATLAB仿真验证了本方法的可行性.     

非线性多滞量延迟微分方程的指数稳定性

收稿研究了一类带多个小滞量的非线性延迟微分方程的指数稳定性,证明了在适当条件下,上述延迟微分方程可保留相应常微分方程的指数稳定性.所获稳定性判据修正和扩展了已有延迟微分方程的相关结果.在文末,数值例子进一步阐明了其稳定性理论.     

基于一类时滞不等式的时滞微分方程的渐近稳定性

利用Lyapunov的方法讨论了时滞微分方程x.(t)=f(t,x(t),x(t-τ(t)))的全局指数渐近稳定性和全局渐近稳定性.     

A multi-agent model describing self-renewal of differentiation effects on the blood cell population

In this work, a new multi-agent model is used to describe blood cell population dynamics. More particularly, we focus our simulations here on differentiation and self-renewal process based on cell communication. We consider the different cases where progenitor cells are able to self-renew or not in the bone marrow. As a consequence of this study, we give some possible explanations of the mechanism for recovery of the system under important blood loss or blood diseases such as anemia.     

Modelling the human immune response dynamics during progression from Mycobacterium latent infection to disease

The use of mathematical tools to study biological processes is of necessity in determining the effects of these biological processes occurring at different levels. In this paper, we study the immune system’s response to infection with the bacteria Mycobacterium tuberculosis (the causative agent of tuberculosis). The response by the immune system is either global (lymph node, thymus, and blood) or local (at the site of infection). The response by the immune system against tuberculosis (TB) at the site of infection leads to the formation of spherical structures which comprised of cells, bacteria, and effector molecules known as granuloma. We developed a deterministic model capturing the dynamics of the immune system, macrophages, cytokines and bacteria. The hallmark of Mycobacterium tuberculosis (MTB) infection in the early stages requires a strong protective cell-mediated naive T cells differentiation which is characterised by antigen-specific interferon gamma (IFN-γ). The host immune response is believed to be regulated by the interleukin-10 cytokine by playing the critical role of orchestrating the T helper 1 and T helper 2 dominance during disease progression. The basic reproduction number is computed and a stability analysis of the equilibrium points is also performed. Through the computation of the reproduction number, we predict disease progression scenario including the latency state. The occurrence of latent infection is shown to depend on a number of effector function and the bacterial load for R₀ < 1. The model predicts that endemically there is no steady state behaviour; rather it depicts the existence of the MTB to be a continuous process progressing over a differing time period. Simulations of the model predict the time at which the activated macrophages overcome the infected macrophages (switching time) and observed that the activation rate (ω) correlates negatively with it. The efficacy of potential host-directed therapies was determined by the use of the model.     

Stability of HIV/HTLV-I co-infection model with delays

In this paper, we formulate a within-host dynamics model for HIV/HTLV-I co-infection under the influence of cytotoxic T lymphocytes (CTLs). The model incorporates silent HIV-infected CD4⁺T cells and silent HTLV-infected CD4⁺T cells. The model includes two routes of HIV transmission, virus to cell (VTC) and cell to cell (CTC). It also incorporates two modes of HTLV-I transmission, horizontal transmission via direct CTC contact and vertical transmission through mitotic division of Tax-expressing HTLV-infected cells. The model takes into account five types of distributed-time delays. We analyze the model by proving the nonnegativity and boundedness of the solutions, calculating all possible equilibria, deriving a set of key threshold parameters, and proving the global stability of all equilibria. The global asymptotic stability of all equilibria is established by utilizing Lyapunov function and LaSalle's invariance principle. We present numerical simulations to justify the applicability and effectiveness of the theoretical results. In addition, we discuss the effect of HTLV-I infection on the HIV dynamics and vice versa.     

高频数据交易量久期与价格变化的动态行为研究

本文基于Log-ACD模型和一类非参数模型,研究了股票价格持续上升时期和价格持续下降时期,交易量久期与价格变化的动态关系。研究表明在不同的市场格局下,价格变化对交易量的影响会有显著区别。另一方面我们发现阈值的选取会影响交易量久期的统计性质,阈值变大时交易量久期的长记忆性会变弱。本文在理论上也有所创新,采用了本文前两位作者提出的新的方法估计Log-ACD模型的参数,该方法在误差服从厚尾分布时具有良好的统计性质。利用新的估计构造了Wald检验统计量,检验价格变化的方向对预期交易量久期是否有显著影响。     

Price caps

Price-cap regulation of AT&T, which became effective on July 1, 1989, is an example of an idea that made its way from economic theory to institutional practice; in this case the process took about seven years. We describe both price-cap regulation and its predecessor — rate-of-return regulation — with particular regard to their incentive properties. We then give the assumptions and conclusions of a theoretical study (in fact a principal-agent model) that bears on the likely effectiveness of price-cap regulation. In the concluding section we describe some aspects of the progress of this idea from theory to practice, and draw tentative conclusions about the conditions that made it possible for this progress to be successfully completed.The views expressed here are the authors', and not necessarily those of AT&T Bell Laboratories.     

兵力增援微分对策优化模型及解法

研究了对抗双方的兵力增援问题，建立了兵力增援微分对策优化理论模型及其最优性条件，给出了兵力增援的最优策略。本研究结果对作战方案的制定，评价和作战指挥决策具有理论指导意义。     

On the extension of involutorial Bol loops

The group theoretical problem of the existence of a system of representativesT of the subgroup H of G such that T consists of conjugacy classes of involutions leads to the theory of Bol loops of exponent 2. In this paper, we develop a theory of extensions of such loops and give two applications of the theory. First, we classify all (left) Bol loops of exponent 2 of order 16; second, we classify all Bol loops of exponent 2 whose right nucleus has index 2. In particular, we give a class of examples of non-nilpotent such Bol loops. The second author was supported by the “János Bolyai” Fellowship, the Blaschke Stiftung and the OTKA grants F030737, T029849.     

A weighted dual porous medium equation applied to image restoration

In this paper, we discuss a weighted dual porous medium equation which could be applied to image restoration. After theoretical analysis based on nonlinear semigroup theory, we give experiments to show the efficiency of this novel model. Copyright © 2013 John Wiley & Sons, Ltd.     

A class of nonlinear parabolic-hyperbolic equations applied to image restoration

In this paper, we discuss a class of nonlinear parabolic-hyperbolic equations which could be applied to image restoration. After theoretical analysis, we give an experimental approach to show the efficiency of this kind of model.     

A constrained interval approach to the generalized distance geometry problem

This paper presents a new approach to the generalized distance geometry problem, based on a model that uses constraint interval arithmetic. In addition to theoretical results, we give some computational experiments that illustrate the better performance of the proposed approach, compared to others from the literature.