Simulation of Spread of Infectious Diseases and Population Mobility in a Deterministic Epidemic Patch Model

Computer simulation models are widely applied in various areas of the health care sector, including the spread of infectious diseases. Patch models involve explicit movements of people between distinct locations. The aim of the present work has been designed and explored a patch model with population mobility between different patches and between each patch and an external population. The authors considered a SIR （susceptible-infected-recovered） scheme. The model was explored by computer simulations. The results show how endemic levels are reached in all patches of the system. Furthermore, the performed explorations suggest that the people mobility between patches, the immigration from outside the system and the infection rate in each patch, are factors that may influence the dynamics of epidemics and should be considered in health policy planning.

Backward bifurcation in a fractional-order and two-patch model of tuberculosis epidemic with incomplete treatment

In this paper,we consider a tuberculosis model with incomplete treatment and extend the model to a Caputo fractional-order and two-patch version with exogenous re-infection among the treated individuals,in which only susceptible individuals can travel freely between the patches.The model has multiple equilibria.We determine conditions that lead to the appearance of a backward bifurcation.The results show that the TB model can have exogenous reinfection among the treated individuals and,at the same time,does not exhibit backward bifurcation.Also,conditions that lead to the global asymptotic stability of the disease-free equilibrium are obtained.In case without reinfection,the model has four equilibria.In this case,the global asymptotic stability of the equilibria is established using the Lyapunov function theory together with the LaSalle invariance principle for fractional differential equations(FDEs).Numerical simulations confirm the validity of the theoretical results.

GLOBAL STABILITY OF EXTENDED MULTI-GROUP SIR EPIDEMIC MODELS WITH PATCHES THROUGH MIGRATION AND CROSS PATCH INFECTION

In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups. As a result, we partially generalize the recent result in the article [16].

Analysis of a multi-patch dynamical model about cattle brucellosis

The dissemination of cattle brucellosis in Zhejiang province of China can be attributed to the transport of cattle between cities within the province. In this paper,an n-patch dynamical model is proposed to study the effect of cattle dispersal on brucellosis spread. Theoretically,we analyze the dynamical behavior of the muti-patch model. For the 2-patch submodel,sensitivity analyses of the basic reproduction number R0 and the number of the infectious cattle in term of model parameters are carried out. By numerical analysis,it is obtained that the dispersal of susceptible cattle between patches and the centralization of infected cattle to the large scale patch can alleviate the epidemic and are in favor of the control of disease in the whole region.

Analytical Polarizable Continuum Model for Wavelets on NURBS Patches

This article concerns the application of wavelet techniques on molecular surfaces constituted of four-sided patches. The Polarizable Continuum Model, which is governed by the Poisson-Boltzmann equation, is treated by means of boundary integral equations. The media inside and outside the molecular surface consist respectively of the solute and the solvent. For a given electrically charged molecule, the principal unknown is the electrostatic solvation energy when the permittivity is specified. The wavelet basis functions are constructed on the unit square which are subsequently mapped onto the patches that are assumed to be isotropically shaped and to admit similar surface areas. The initial transmission problem is recast as an integral equation in term of both the single and the double layers. Domain decomposition preconditioner serves as acceleration of the linear solver of the single layer which is badly conditioned.

Assessment of the Sensitivity of Streamflow Simulations to Changes in Patch Resolution Using GIS Based Hydro-Ecologic Model

Eight different patch configurations were investigated to analyze the effect of patch characterization/formation in streamflow simulation, using the Regional Hydro-Ecologic Simulation Systems (RHESSys) model. It is investigated for eight different patch configurations of a subcatchment of the Turkey Lakes Watershed, Ontario. The model’s hydrological parameters are calibrated for each of these patch configurations and the performance of the simulations is evaluated. Results indicate that both the nature of the flow simulation and the calibrated parameter values are sensitive to patch configuration. The best simulation results were obtained for the patch configuration with the highest spatial variation of climate, stream network and hillslope conditions across the subcatchment. Different patch configurations also lead to markedly different calibrations of the model’s hydrological parameters (54.26 < k < 119.13;and 1.02 < m < 2.28), which has implications for the physical interpretation and transferability of the calibrated parameter values.

基于Patch-Dynamics模式的土地覆被变化预测——以北京市为例

利用北京市土地利用变化数据建立了Patch-dynamics动力模型。模拟结果表明了在不同的时间尺度上耕地所占比例都持续下降,城镇建设用地、林地所占比例继续上升。由于该模式考虑了模拟对象的变化过程以及不同土地利用类型之间的相互影响,其模拟结果比一般的简单动力模型模拟效果好。通过与实际情况的比较检验,用1996年数据对2001年的模拟结果与实际差别不大,误差在0~0.05之间,对于面积较小地类的模拟误差较小,说明这个方法可以用来对未来的土地利用变化状况进行模拟、预测。然而,这个模型只适应于十年尺度的预测,模拟时间越长,误差越大。在此基础上,提出协调土地利用矛盾,维持一定规模的城市绿色空间,实现首都城市定位目标的建议。

Multiwavelet Boundary Element Method for Cavities Admitting Many NURBS Patches

We consider the modeling and simulation by means of multiwavelets on many patches. Our focus is on molecular surfaces which are represented in the form of Solvent Excluded Surfaces that are featured by smooth blendings between the constituting atoms. The wavelet bases are constructed on the unit square which maps bijectively onto the patches embedded in the space. The cavity which designates the surface bounding a molecular model is acquired from the nuclei coordinates and the Van-der-Waals radii. We use multi-wavelets for which the wavelet basis functions are organized hierarchically on several levels. Our assembly of the linear system is accomplished by using a hierarchical tree which enables the treatment of large molecules admitting thousands of patches. Along with the patch construction, some wavelet simulation outcomes which are applied to realistic patches are reported.

基于引导扩散模型的自然对抗补丁生成方法

近年来,物理世界中的对抗补丁攻击因其对深度学习模型安全的影响而引起了广泛关注.现有的工作主要集中在生成在物理世界中攻击性能良好的对抗补丁,没有考虑到对抗补丁图案与自然图像的差别,因此生成的对抗补丁往往不自然且容易被观察者发现.为了解决这个问题,本文提出了一种基于引导的扩散模型的自然对抗补丁生成方法.具体而言,本文通过解析目标检测器的输出构建预测对抗补丁攻击成功率的预测器,利用该预测器的梯度作为条件引导预训练的扩散模型的逆扩散过程,从而生成自然度更高且保持高攻击成功率的对抗补丁.本文在数字世界和物理世界中进行了广泛的实验,评估了对抗补丁针对各种目标检测模型的攻击效果以及对抗补丁的自然度.实验结果表明,通过将所构建的攻击成功率预测器与扩散模型相结合,本文的方法能够生成比现有方案更自然的对抗补丁,同时保持攻击性能.

Robust Boolean Operation for Sculptured Models

To enhance the ability of current modeling system, an uniformed representation is designed to represent wire frame, solid, surface models. We present an algorithm for Boolean operation between the models under this representation. Accuracy, efficiency and robustness are the main consideration. The geometric information is represented with trimmed parametric patches and trimmed parametric splines. The topological information is represented with an extended half edge data structure. In the process of intersection calculation, hierarchy intersection method is applied for unified classification. Tracing the intersection curve to overcome degenerate cases that occur frequently in practice. The algorithm has been implemented as the modeling kernel of a feature based modeling system named GS CAD98, which was developed on Windows/NT platform.

实测轮轨蠕滑曲线对钢轨磨耗影响分析

轮轨蠕滑曲线会影响轮轨动态相互作用,进而影响钢轨磨耗,为研究实测轮轨蠕滑曲线对钢轨磨耗的影响,首先,基于最小二乘法获得适用于Polach模型和修改FASTSIM算法的参数,模拟40~400 km/h行车速度范围内的实测蠕滑曲线;随后,在SIMPACK软件中建立车辆系统动力学模型,并通过Polach模型测得实测蠕滑曲线;最后,采用Kik-Piotrowski模型和修改的FASTSIM算法进行轮轨非赫兹滚动接触计算,并结合USFD磨耗模型预测钢轨磨耗,对比了理想与实测蠕滑曲线条件下钢轨磨耗的差异.研究表明:理想蠕滑曲线条件下钢轨磨耗深度明显大于实测蠕滑曲线下的结果,随着车辆通过次数的增加,理想条件下钢轨磨耗分布范围更大,内外轨磨耗分布范围分别为实测蠕滑曲线的1.5倍和1.3倍;摩擦系数和磨耗率显著影响钢轨磨耗大小及磨耗分布情况,故在车辆动力学仿真和钢轨磨耗计算中有必要考虑实测轮轨蠕滑曲线;形成了确定实测蠕滑曲线参数的前处理程序,可服务于车辆动力学仿真和钢轨磨耗计算,可以有效指导现场进行钢轨打磨等养护维修工作.

Constructing M-sided Patches with NURBS

The paper first summarizes the development of generating N-sided surface patches , andthen proposes a method of constructing general N-sided patches whose boundary curves and crossderivatives are Bspline curves of degree 3. The patch constructed is made up of n rectangularNURBS subpatches of degrees 7 ×7. The method is implemented in two steps : first , an N-sidedGregory patch is constructed, then, using our recent research on blended B-spline surface, nrectangular NURBS subpatches of degrees 7×7 are constructed to form an Nsided patch in termsof the data calculated in the first step. At the end of the paper , conclusions and some examples aregiven.

2013―2021年南京热环境时空演化及扩张驱动机制研究

基于Landsat 8 OLI-TIRS遥感影像,利用辐射方程算法反演得到南京市地表温度数据。从数量和速度方面揭示南京市2013―2021年间热环境景观的时空变化特征,并进一步利用核密度分析和空间质心迁移轨迹揭示热环境景观的空间演变特征。此外,借助PLUS模型探究了2013―2021年热环境景观的驱动机制。结果表明:(1)2013―2021年间中温区景观在研究区占主导地位,其中2017―2021年热环境景观变化最强烈,其综合热环境动态度为23.94%。(2)低温区的核密度高值主要位于水域和林地,北部集聚特征较为明显;次低温区的核密度分布特征表现为北部和南部较密集且破碎化明显;中温区的核密度分布呈“中间少四周多”的格局;次高温区景观呈多核心增长的趋势;高温区景观集聚特征最为显著,主要分布于长江两岸及各市区的中心地区。(3)低温区质心迁移速度最快,整体上向东北方向移动了21.30 km;次低温区质心迁移速度由慢到快,先向西北移动9.52 km,后向东南移动17.88 km;高温区、次高温区、中温区质心整体向西南方向偏移,移动距离分别为19.99、4.77、4.04 km。(4)从不同热环境景观扩张的驱动因子来看,低温区、次低温区和中温区扩张的驱动力主要是受高程的影响,次高温区和高温区扩张的驱动力主要是距住宅距离和距工厂距离。本研究对于加强南京地表热环境的监测和促进城市生态环境可持续发展具有重要的参考意义。

基于高时空分辨率数据的上栗县植被NPP估算及分析

针对目前植被净初级生产力(NPP)像素级的研究成果缺乏对地理空间细节的描述这一问题,借助中高分遥感影像,利用深度学习模型获取精确地类图斑,将栅格化结果作为改进的CASA模型的输入参数,最终估算得到上栗县不同植被类型的地块级NPP值。结果表明,1)相比于传统的只利用影像光谱特征提取的方法,深度学习技术获取的地类图斑更为准确。同时,在林地图斑的基础上,结合中分影像对林地类型进行判别,林地分类精度为91.3134%。说明中高分遥感影像结合,能够较好地在区县尺度上开展植被的精细分类。2)以CASA模型理论为基础,对模型中的最大光年利用率的取值进行修正。同时以地类图斑的栅格化结果作为模型的输入参数,剔除了建筑区、道路、裸地等无植被覆盖区对模型计算的影响,并对估算结果与其他模型估算结果进行比较与验证,证明了试验结果的准确性。3)实现了上栗县NPP结果在空间上的精细化表达,研究结果具备良好的空间细节特征,不仅满足了面积统计、定性分析等简单需求,还可为后续碳循环、碳源/汇等研究提供客观、定量化的数据支撑。

刚性植物对聚焦波爬坡影响的数值模拟

基于开源程序非静压模型NHWAVE(Non-Hydrostatic Water Wave Model),建立了高精度二维数值波浪水槽,系统研究了非淹没刚性植物对聚焦波爬坡的影响规律,并分析了有效波高、植物区密度和长度等因素对局部最大波高衰减系数、总波能耗散系数和最大波浪爬高的影响。研究结果表明:当聚焦波向岸传播时,局部最大波高衰减系数和总波能耗散系数均随有效波高、植物区密度和植物区长度的增大而增大。聚焦波的最大爬高随有效波高的增大而增大,随植物区密度和植物区长度的增大而减小。随着植物区密度和长度的增大,波峰聚焦的聚焦波相比波谷聚焦的聚焦波有着更大的最大波浪爬高。结果可为进一步认识沿岸防浪林对聚焦波浪的衰减效应和沿海地区的防灾减灾建设提供参考依据。

基于PLUS-InVEST模型的“两湖一库”流域水质净化时空演变

探讨土地利用变化所引发的水质净化演变,对于保护和改善水质,实现可持续发展具有重要意义。以“两湖一库”流域为例,运用PLUS(patch-level land use simulation)模型和InVEST(integrated valuation of ecosystem services and tradeoffs)模型生态系统服务水质净化模块,基于2000年、2010年和2020年土地利用数据,模拟流域在未来自然发展情景和生态保护情景下的用地类型时空格局变化以及水质净化特征。定量揭示土地利用变化与水质净化功能的响应关系。结果表明:“两湖一库”流域土地类型以耕地为主,2030年在自然发展情景下耕地、林地、草地面积呈下降趋势,建设用地呈上升趋势,生态保护情景可有效保护流域耕地、林地等空间分布和面积;“两湖一库”流域TN、TP输出量以低强度输出为主,2000—2020年TN输出量先增加后减少,TP输出量逐年增加,水质净化能力呈稳中变好的趋势;2030年自然发展情境下TN输出量持续减少,TP输出量呈向上浮动,生态保护情景下TN、TP输出量较自然发展情景下减少,生态保护情景可以增加水质净化能力。生态用地类型可以有效截留N、P进入水体,生态保护情景下有效降低生态用地类型的变化速度,减少TN、TP的输出量,“两湖一库”流域未来规划中应增加生态用地的占比,增加土地类型对TN、TP的截留能力。

一类具有预防意识的多斑块SEIQR传染病模型的阈值动力学研究

结合一般传染病病毒传播的特点,提出了一类具有预防意识和斑块间流动感染的SEIQR传染病传播动力学模型.根据下一代矩阵法算出了单斑块下疾病传播的阈值R_(a)和两斑块下疾病传播的阈值R_(a)^(φ),得到当R_(a)≤1时单斑块下无病平衡点全局渐近稳定和R_(a)^(φ)≤1时两斑块下无病平衡点局部稳定的结论,数值模拟证实了理论结果.敏感性分析说明了参数对基本再生数的影响,结果表明增加人群预防意识能够抑制病毒在斑块间的传播,但群体在斑块间流动时发生感染会加剧病毒的传播.

具有弱Allee效应的三斑块捕食-食饵扩散模型动力学分析

本文建立一类具有弱Allee效应的三斑块捕食-食饵扩散模型,并研究食饵的Allee效应和食饵的扩散对模型正平衡点的存在性及稳定性的影响.首先,分析了模型永久持续生存的充分条件.其次,利用图理论构造出新的Lyapunov函数,得到模型正平衡点是全局渐近稳定的充分条件.最后利用Matlab软件对分析结果进行数值验证.

穴位贴敷疗法对失眠障碍患者PSQI改善率临床预测模型的建立与验证

目的:构建穴位贴敷对失眠障碍(ID)患者PSQI改善率结局影响因素的临床预测模型,为穴位贴敷疗法改善ID患者的失眠结局提供预测的思路及方法。方法:采用回顾性队列研究方法,收集2019年6月~2020年6月于中国中医科学院针灸医院、丰体时代社区卫生服务站两个中心接受穴位贴敷疗法治疗的64例ID患者0周、1周、2周、3周、4周、6周的临床资料(2例剔除,共372例数据)。采用单因素Logistic回归分析、向前向后逐步回归分析用于筛选构建列线图预测模型的变量,根据最小赤池信息准则(AIC)选定最优模型,进一步根据筛选出最优模型因素的回归系数利用R语言中的“rms”包构建列线图预测模型,并通过受试者工作特征曲线(ROC)下面积(AUC)评估模型的区分度,校准曲线和Hosmer-Lemeshow拟合优度检验评估校准度,利用“Bootstrap重复抽样法”对模型进行内部验证。结果:①治疗时间、病程≤12月、12月<病程≤36月、疲劳程度、既往是否使用促眠药物、一般健康状况、社会功能、躯体疼痛、肝郁化火组合AIC为300.31,为最优模型,方差膨胀因子(VIF)均<5,容忍度均>0.5,提示多重共线性的可能性较小,是穴位贴敷疗法对ID患者失眠结局的独立预测因素;②预测模型的ROC曲线下面积AUC为[0.856,95%CI(0.814,0.898)],说明该预测模型具有较好的区分度;各变量因素单独预测结局事件的ROC曲线下面积AUC位于0.5至0.8之间,均低于联合预测结局事件的AUC值,表明联合预测较各变量因素单独预测具有更好的区分度及预测能力;③校准曲线显示预测模型的拟合曲线与理想曲线较为接近,表明该模型具有较好的校准度;④Brier得分为[0.125,95%CI(0.105,0.145)],说明该预测模型总体预测性能较好;Hosmer-Lemeshow拟合优度检验显示P=0.152(P>0.05),提示该模型拟合良好。结论:以治疗时间、病程≤12月、12月<病程≤36月、疲劳程度、既往是否使用促眠药物、一般健康状况、社会功能、躯体疼痛、肝郁化火构建的临床预测模型具有较好的预测效能,可为穴位贴敷疗法治疗失眠障碍的临床决策提供一定的参考价值。

具有饱和发生率的多斑块传染病模型的动力学分析

建立了一类斑块环境下具有饱和发生率的SVEIQR传染病模型,该模型考虑了疫苗接种和隔离策略.首先,通过构造再生矩阵得到了基本再生数R0的矩阵表示.然后,应用Lyapnuov函数法证明了当R0<1时无病平衡点的全局渐近稳定性.最后,对R0进行了敏感性分析和数值模拟.结果表明:增加接种率和隔离率都能够减少基本再生数的大小;人口从高风险地区到低风险地区迁移率增加能够增大基本再生数的值.所以,当疾病爆发后,应严格控制高风险地区的人口向外流动,并及时进行疫苗接种以及采取相应的隔离策略.