sensitivity analysis

敏感性分析
  • 文章类型: Journal Article
    在中国,数条高速公路被设计为带有铰链连接的预制箱涵,与其他国家的预制涵洞具有不同的结构特征。这种差异将有助于预制箱涵的涵洞-土相互作用,这可能会影响涵洞上的土压力。基于现场试验和数值模拟的方法,研究了跨度为4m,上升为4m的铰链式预制箱涵(HPBC),适用于中国的西渝高速公路。本研究的目的是通过现场测试,研究HPBC涵洞顶板在不同回填高度的垂直土压力。采用FLAC3D软件对回填高度的影响进行了进一步分析,回填模数,HPBC顶板垂直土压力的基础模量。还检查了HPBC和整体式箱涵(MBC)之间的差异。此外,提出了一种修正的顶板垂直土压力计算方法,并与AASHTO方法进行了比较,该方法用于计算涵洞顶部的土压力以及中国涵洞设计规范中的值。所提出的方法能够提高土压力法的精度,使其更能代表实际情况。随后,回填高度的敏感性分析,利用正交阵列分析原理和本文提出的改进计算方法,对顶板竖向土压力集中系数进行了回填模量和地基模量的计算。这项研究的结果为HPBC涵洞顶部土压力的确定提供了有价值的见解。
    In China, several expressways have been designed as prefabricated box culverts with hinge connections, which have different structural features from the prefabricated culverts in other countries. The difference would contribute to the culvert-soil interaction of prefabricated box culverts, which could affect the earth pressure on the culvert. Based on the field test and numerical simulation method, a hinged prefabricated box culvert (HPBC) with a span of 4 m and a rise of 4 m was investigated, which was applied to the Xi-Yu expressway in China. The objective of this research was to investigate the vertical earth pressure on the top slab of the HPBC culvert at different backfill heights through the field tests. The FLAC3D software was employed to conduct further analysis of the effects of backfill height, backfill modulus, and foundation modulus on the vertical earth pressure on the top slab of HPBC. The differences between the HPBC and monolithic box culvert (MBC) were also examined. Furthermore, a revised method for calculating the vertical earth pressure on the top slab was put proposed and compared with the AASHTO method for calculating earth pressure on the top of culverts and the values taken from the Chinese culvert design code. The proposed method is capable of improving the accuracy of the earth pressure approach, making it more representative of actual conditions. Subsequently, the sensitivity analysis of backfill height, backfill modulus and foundation modulus to the vertical earth pressure concentration coefficient of the top slab was carried out by using the principle of orthogonal array analysis and the modified calculation method proposed in this paper. The findings of this study offer valuable insights into the determination of culvert top earth pressure of HPBC.
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  • 文章类型: Journal Article
    在虚拟生物等效性(VBE)评估中,根据体外数据和小型临床试验数据验证的药代动力学模型用于模拟其他不可行的大型试验。模拟VBE试验在频率论框架中进行评估,就好像它们是真实的,尽管它们可以使用无限数量的虚拟受试者。这可以充分控制消费者风险,但给生产者带来不必要的风险。我们提出了一个完全贝叶斯模型集成的VBE评估框架,以规避这些限制。
    我们通过对假设的帕潘立酮棕榈酸酯(PP)通用长效注射混悬液制剂的案例研究来说明我们的方法,该制剂使用针对参考制剂发布的经过验证的群体药代动力学模型。BE测试,学习力,I型和II型误差分析或其贝叶斯等价物,并演示了安全空间分析。
    完全贝叶斯的工作流程比频率更精确。两个工作流程中关于生物等效性和安全空间分析的决定可能会明显不同,因为贝叶斯分析更准确。
    贝叶斯框架可以充分控制消费者风险并最大程度地降低生产者风险。它奖励数据收集和模型集成,以充分利用先验信息。频率论方法不太精确,但计算速度更快,它仍然可以用作缩小参数空间的第一步,以便在安全空间分析中进行探索。
    UNASSIGNED: In virtual bioequivalence (VBE) assessments, pharmacokinetic models informed with in vitro data and verified with small clinical trials\' data are used to simulate otherwise unfeasibly large trials. Simulated VBE trials are assessed in a frequentist framework as if they were real despite the unlimited number of virtual subjects they can use. This may adequately control consumer risk but imposes unnecessary risks on producers. We propose a fully Bayesian model-integrated VBE assessment framework that circumvents these limitations.
    UNASSIGNED: We illustrate our approach with a case study on a hypothetical paliperidone palmitate (PP) generic long-acting injectable suspension formulation using a validated population pharmacokinetic model published for the reference formulation. BE testing, study power, type I and type II error analyses or their Bayesian equivalents, and safe-space analyses are demonstrated.
    UNASSIGNED: The fully Bayesian workflow is more precise than the frequentist workflow. Decisions about bioequivalence and safe space analyses in the two workflows can differ markedly because the Bayesian analyses are more accurate.
    UNASSIGNED: A Bayesian framework can adequately control consumer risk and minimize producer risk . It rewards data gathering and model integration to make the best use of prior information. The frequentist approach is less precise but faster to compute, and it can still be used as a first step to narrow down the parameter space to explore in safe-space analyses.
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  • 文章类型: Journal Article
    社区和医院的耐甲氧西林金黄色葡萄球菌(MRSA)病例数量在全球范围内呈上升趋势。在这项工作中,建立了社会中MRSA感染动态的非线性确定性模型,以可视化意识在干预措施中的重要性,该干预措施可用于在有和没有最佳控制的情况下预防传播。验证了所提出的腐败模型的积极性和唯一性,以识别社会中感染因素的解决水平。此外,通过数学技术和图形,探讨了各种参数如何影响生殖数R0,并对所提出的模型进行了敏感性分析。利用带有一阶导数检验的Lyapunov函数建立了模型均衡分析的全局稳定性。在该模型中,从由MRSA住院患者和门诊患者组成的私立医院收集的总共七年的数据用于数值模拟,并通过使用非标准有限差分(NSFD)方案观察感染动态。当最优控制作为第二个模型应用时,确定提高手卫生意识和戴口罩是预防社区获得性MRSA(CA-MRSA)和医院获得性MRSA(HA-MRSA)传播的关键控制措施.最后,结论是社区中CA-MRSA和HA-MRSA病例均呈上升趋势,提高对传播的认识对于防止进一步传播极为重要。
    The number of Methicillin-resistant Staphylococcus aureus (MRSA) cases in communities and hospitals is on the rise worldwide. In this work, a nonlinear deterministic model for the dynamics of MRSA infection in society was developed to visualize the significance of awareness in interventions that could be applied in the prevention of transmission with and without optimal control. Positivity and uniqueness were verified for the proposed corruption model to identify the level of resolution of infection factors in society. Furthermore, how various parameters affect the reproductive number R 0 and sensitivity analysis of the proposed model was explored through mathematical techniques and figures. The global stability of model equilibria analysis was established by using Lyapunov functions with the first derivative test. A total of seven years of data gathered from a private hospital consisting of inpatients and outpatients of MRSA were used in this model for numerical simulations and for observing the dynamics of infection by using a non-standard finite difference (NSFD) scheme. When optimal control was applied as a second model, it was determined that increasing awareness of hand hygiene and wearing a mask were the key controlling measures to prevent the spread of community-acquired MRSA (CA-MRSA) and hospital-acquired MRSA (HA-MRSA). Lastly, it was concluded that both CA-MRSA and HA-MRSA cases are on the rise in the community, and increasing awareness concerning transmission is extremely significant in preventing further spread.
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  • 文章类型: Journal Article
    水资源的高质量发展支撑着社会经济的高质量发展。高质量发展连接高质量生活,明确小流域的重点管理内容,对建设生态清洁小流域,促进区域生产生活具有重要作用。以前关于污染负荷的研究侧重于研究各种外部驱动因素对污染负荷的影响,但仍缺乏关于污染源本身变化对污染负荷影响的研究。在这项研究中,敏感性分析用于确定不同来源的变化对总污染负荷的影响,可以识别关键污染源。我们首先采用污染物排放系数法对2010年至2021年tu江上游流域小流域的非点源污染负荷进行了量化。然后,Getis-OrdGi*的组合敏感性分析用于识别全球的关键来源及其关键领域,区(县),和城镇(街道)尺度,分别。结果表明:(1)COD的污染负荷,NH3-N,TN,TP都呈下降趋势,减少18.3%,16.2%,18.6%,2010年至2021年分别为28.1%;(2)畜禽养殖污染源是整个流域大多数地区最关键的污染源;(3)高危区域主要集中在靖阳区及其下属乡镇(街道)。有低污染风险区域向高污染风险区域过渡的趋势,高风险地区主要集中在东南部,并表现出明显的污染负荷溢出现象。这项研究可以促进其他类似的小流域,对小流域面源污染控制具有重要意义。
    High-quality development of water resources supports high-quality socio-economic development. High-quality development connects high-quality life, and clarifying the key management contents of small watersheds plays an important role in building ecologically clean small watersheds and promoting regional production and life. Previous research on pollution loads has focused on examining the impact of various external drivers on pollution loads but still lacks research on the impact of changes in pollution sources themselves on pollution loads. In this study, sensitivity analysis was used to determine the impact of changes from different sources on the total pollution loads, which can recognize the critical pollution sources. We first employed the pollutant discharge coefficient method to quantify non-point source pollution loads in the small watershed in the upstream Tuojiang River basin from 2010 to 2021. Then, combination sensitivity analysis with Getis-Ord Gi* was used to identify the critical sources and their crucial areas at the global, districts (counties), and towns (streets) scales, respectively. The results indicate: (1) The pollution loads of COD, NH3-N, TN, and TP all show a decreasing trend, reducing by 18.3%, 16.2%, 18.6%, and 28.1% from 2010 to 2021, respectively; (2) Livestock and poultry breeding pollution source is the most critical source for majority areas across watershed; (3) High-risk areas are mainly concentrated in Jingyang district and its subordinate towns (streets). There is a trend of low-pollution risk areas transitioning to high-pollution risk areas, with high-risk areas predominantly concentrated in the southeast and exhibiting a noticeable phenomenon of pollution load spilling around. This study can promote other similar small watersheds, holding significant importance for non-point source pollution control in small watersheds.
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  • 文章类型: Journal Article
    这项研究介绍了一种新颖的方法,用于开发为健康风险评估量身定制的高级暴露概念模型,专注于微环境。
    该研究是在中国的一家大型冶炼厂进行的,目的是评估与设施和周围土壤中的痕量金属(TM)污染物相关的健康风险。
    确定性风险评估表明,钴,镉,锑,锰,砷,plumbum,和汞(Co,Cd,Sb,Mn,As,Pb,和Hg)需要通过概率风险评估进行进一步评估,以评估居民的潜在健康风险。发现其他TM的95%分位数浓度在可接受的健康风险范围内。对于概率风险评估,暴露参数,如体重,呼吸频率,和暴露持续时间使用问卷收集。对住宅微环境的有针对性的评估显示,它是致癌风险(CR)和非致癌风险(NCR)最高的场所。值范围分别为2.84×10-5至6.7×10-5和1.59至5.57。
    在住宅和工业区中构成最大健康风险的主要污染物已被确定为As,Pb,和Mn。概率健康风险模型,关注微环境因素,产生更精确的结果,并为管理土壤健康风险提供了有价值的工具。
    UNASSIGNED: This study introduces a novel method for developing an advanced exposure conceptual model tailored for health risk assessment, focusing on microenvironments.
    UNASSIGNED: The research was conducted at a major smelter in China to assess the health risks associated with trace metals (TMs) pollutants in the facility and the surrounding soil.
    UNASSIGNED: Deterministic risk assessment indicated that cobalt, cadmium, antimony, manganese, arsenic, plumbum, and mercury (Co, Cd, Sb, Mn, As, Pb, and Hg) necessitated further evaluation through probabilistic risk assessment to assess potential health risks to residents. The 95% quantile concentrations of other TMs were found to be within acceptable health risk limits. For the probabilistic risk assessment, exposure parameters such as body weight, respiration rate, and exposure duration were collected using a questionnaire. This targeted assessment of the residential microenvironment revealed it as the site of the highest carcinogenic (CR) and non-carcinogenic risks (NCR), with values ranging from 2.84×10-5 to 6.7×10-5 and 1.59 to 5.57, respectively.
    UNASSIGNED: The primary contaminants posing the greatest health risks in residential and industrial areas have been identified as As, Pb, and Mn. The probabilistic health risk model, which focuses on microenvironmental factors, yields more precise results and offers a valuable tool for managing soil health risks.
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  • 文章类型: Journal Article
    气候变化对溶解氧(DO)浓度有重大影响,特别是在发生许多人类活动的沿海入口。由于各种水质(WQ),水文,以及影响这种现象的气候参数,预测和建模DO变化是一个具有挑战性的过程。因此,这项研究引入了一种创新的深度学习神经网络(DLNN)方法来建模和预测埃及拉希德沿海入口的DO浓度,利用现场记录的WQ和水文气候数据集。最初,进行统计和探索性数据分析,以全面了解DO波动与相关WQ和气候压力源之间的关系。作为开发有效DO预测模型的第一步,传统的机器学习(ML)方法,如高斯过程回归(GPR),支持向量回归(SVR)并采用决策树回归器(DTR)。随后,DLNN方法用于验证所研究的常规ML方法的预测能力。最后,进行了敏感性分析,以评估WQ和水文气候参数对预测DO的影响。结果表明,与表现最好的ML方法相比,DLNN显著提高了DO预测精度4%,相关系数为0.95,均方根误差(RMSE)为0.42mg/l。太阳辐射(SR),pH值,水位(WL),和大气压力(P)是影响DO波动的最重要的水文气候参数。最终,开发的模型可以作为沿海当局监测埃及沿海加速气候变化导致的DO变化的有效指标。
    Climate change has a significant impact on dissolved oxygen (DO) concentrations, particularly in coastal inlets where numerous human activities occur. Due to the various water quality (WQ), hydrological, and climatic parameters that influence this phenomenon, predicting and modeling DO variation is a challenging process. Accordingly, this study introduces an innovative Deep Learning Neural Network (DLNN) methodology to model and predict DO concentrations for the Egyptian Rashid coastal inlet, leveraging field-recorded WQ and hydroclimatic datasets. Initially, statistical and exploratory data analyses are performed to provide a thorough understanding of the relationship between DO fluctuations and associated WQ and hydroclimatic stressors. As an initial step towards developing an effective DO predictive model, conventional Machine Learning (ML) approaches such as Gaussian Process Regression (GPR), Support Vector Regression (SVR), and Decision Tree Regressor (DTR) are employed. Subsequently, a DLNN approach is utilized to validate the prediction capabilities of the investigated conventional ML approaches. Finally, a sensitivity analysis is conducted to evaluate the impact of WQ and hydroclimatic parameters on predicted DO. The outcomes demonstrate that DLNN significantly improves DO prediction accuracy by 4% compared to the best-performing ML approach, achieving a Correlation Coefficient of 0.95 with a root mean square error (RMSE) of 0.42 mg/l. Solar radiation (SR), pH, water levels (WL), and atmospheric pressure (P) emerge as the most significant hydroclimatic parameters influencing DO fluctuations. Ultimately, the developed models could serve as effective indicators for coastal authorities to monitor DO changes resulting from accelerated climate change along the Egyptian coast.
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  • 文章类型: Systematic Review
    人们已经认识到,与艾滋病毒相关的污名阻碍了检测工作,治疗,和预防。在这次系统审查中,我们的目的是总结艾滋病毒相关的污名和年龄之间的关联的现有发现,社会支持,教育状况,抑郁症,就业状况,财富指数,性别,residence,关于艾滋病毒的知识,婚姻状况,自诊断以来的持续时间,和披露状况使用了大量的研究。
    电子数据库,包括Scopus,Medline/PubMed,WebofSciences(WOS),科克伦图书馆,谷歌学者,和开放研究数据集挑战进行了系统搜索,直到2023年4月15日。我们包括了各种艾滋病毒污名研究,不管语言,发布日期,或地理位置。40项研究符合纳入标准,共有171627名患者。使用混合效应模型来汇集估计值和评估发表偏差,以及进行敏感性分析。
    年龄等因素,社会支持,高等教育,更高的社会经济地位,良好的艾滋病毒知识,和更长的艾滋病毒感染年限显著降低了与艾滋病毒相关的耻辱的可能性。相反,抑郁等因素,居住在农村地区,女性受访者,和未披露HIV状况与HIV相关污名的高风险显著相关.
    为了对抗与艾滋病毒相关的系统性耻辱,通过提高社区一级的艾滋病毒认识,发展健康和全面的社会方法至关重要。除了激进主义,地方经济发展对于建立具有强大社会结构的繁荣社区也至关重要。
    UNASSIGNED: It has been recognized that HIV-related stigma hinders efforts in testing, treatment, and prevention. In this systematic review, we aimed to summarize available findings on the association between HIV-related stigma and age, social support, educational status, depression, employment status, wealth index, gender, residence, knowledge about HIV, marital status, duration since diagnosis, and disclosure status using a large number of studies.
    UNASSIGNED: Electronic databases including Scopus, Medline/PubMed, Web of Sciences (WOS), Cochrane Library, Google Scholar, and Open Research Dataset Challenge were systematically searched until 15 April 2023. We included all kinds of HIV-stigma studies, regardless of language, publishing date, or geographic location. The inclusion criteria were met by 40 studies, with a total of 171,627 patients. A mixed-effect model was used to pool estimates and evaluate publication bias, as well as to conduct sensitivity analysis.
    UNASSIGNED: Factors such as older age, social support, greater education, higher socioeconomic status, good knowledge of HIV, and longer years of living with HIV significantly lowered the likelihood of HIV-related stigma. Contrarily, factors such as depression, residing in rural areas, female respondents, and non-disclosure of HIV status were significantly associated with a high risk of HIV-related stigma.
    UNASSIGNED: To combat systemic HIV-associated stigma, it is crucial to develop wholesome and comprehensive social methods by raising community-level HIV awareness. In addition to activism, local economic development is also crucial for creating thriving communities with a strong social fabric.
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  • 文章类型: Journal Article
    地下水在满足不同需求方面的关键作用,包括喝酒,工业,农业,强调了有效资源管理的紧迫性。过量的地下水开采,特别是在沿海地区,包括伊朗西北部的Urmia平原,破坏含水层内淡水和盐水边界之间的平衡。控制海水入侵的影响参数-地下水发生(G),含水层导水率(A),地下水位高于平均海平面的高度(L),与海岸的距离(D),海水入侵现状的影响(I),和饱和含水层的厚度(T)-合并以形成沿海含水层的GALDIT脆弱性指数。这项研究通过结合两个额外的水文地质变量:水力梯度(i)和抽水率(P)来丰富GALDIT框架。此扩展生成了七个不同的漏洞图(GALDIT,GAIDIT,GAIDIT-P,GALDIT-i,GALDIT-iP,GALDIT-P,GAPDIT).在Urmia平原,传统的GALDIT指数显示的脆弱性值从2到8.1不等,分为从微不足道到非常高的六类脆弱性。然而,修改后的指数,GAiDIT和GAiDIT-P,产生三级分类,从低到高的脆弱性。在GALDIT-i和GALDIT-iP中引入\"i\"和\"P\"参数,提高了漏洞映射的精度,改变类分布和加强脆弱性评级。东方,中央,Urmia平原的沿海地区显示出高到非常高的脆弱性水平,与西部地区的脆弱性较低相反。GALDIT-P(r=0.82)和GALDIT-iP(r=0.81)指数均与Cl浓度有很强的相关性,从而提高了比传统的GALDIT指数(r=0.72)的映射精度。敏感性分析突出了“i”参数的关键影响,建议应修改其权重。参数重新校准用于放大“G”的重要性,\"\"L,\"\"D,\"和\"i\"参数,同时减少其他人。多个水文地质变量的集成大大提高了地下水脆弱性评估的精度。
    The critical role of groundwater in meeting diverse needs, including drinking, industrial, and agricultural, highlights the urgency of effective resource management. Excessive groundwater extraction, especially in coastal regions including Urmia Plain in NW Iran, disrupts the equilibrium between freshwater and saline boundaries within aquifers. Influential parameters governing seawater intrusion-groundwater occurrence (G), aquifer hydraulic conductivity (A), the height of groundwater level above the mean sea level (L), distance from the shore (D), impact of the existing status of seawater intrusion (I), and thickness of the saturated aquifer (T)-merge to shape the GALDIT vulnerability index for coastal aquifers. This study enriches the GALDIT framework by incorporating two additional hydrogeological variables: hydraulic gradient (i) and pumping rate (P). This expansion produces seven distinct vulnerability maps (GALDIT, GAiDIT, GAiDIT-P, GALDIT-i, GALDIT-iP, GALDIT-P, GAPDIT). In the Urmia Plain, the traditional GALDIT index reveals vulnerability values ranging from 2 to 8.1, categorized into six classes from negligible to very high vulnerability. However, the modified indices, GAiDIT and GAiDIT-P, yield a three-class categorization, ranging from low to high vulnerability. The introduction of the \"i\" and \"P\" parameters in GALDIT-i and GALDIT-iP enhances the precision of vulnerability mapping, altering class distribution and intensifying vulnerability ratings. The eastern, central, and coastal areas of the Urmia Plain demonstrate high to very high vulnerability levels, in contrast to the lower vulnerability observed in the western regions. Both the GALDIT-P (r = 0.82) and GALDIT-iP (r = 0.81) indices show strong correlations with Cl concentration, thereby improving mapping accuracy over the traditional GALDIT index (r = 0.72). A sensitivity analysis highlights the critical influence of the \"i\" parameter, suggesting its weighting should be revised. Parameter recalibration serves to amplify the significance of \"G,\" \"L,\" \"D,\" and \"i\" parameters, while diminishing others. The integration of multiple hydrogeological variables considerably enhances the precision of groundwater vulnerability assessments.
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  • 文章类型: Journal Article
    这项研究旨在制定一个数学框架,以研究拉萨病毒如何在相反性别的人类中传播。在没有拉沙热的情况下,在平衡点分析模型的稳定性。使用现实生活中的数据评估模型的有效性,并估计确定基本再现数所需的所有参数。进行敏感性分析以查明显着影响感染传播的关键参数。模拟了阈值参数与基本再现数之间的相互作用。控制论被用来设计和评估策略,比如提高认识运动,提倡使用避孕套,并部署灭鼠剂以有效减少病毒传播的可能性。
    This study aims to formulate a mathematical framework to examine how the Lassa virus spreads in humans of opposite genders. The stability of the model is analyzed at an equilibrium point in the absence of the Lassa fever. The model\'s effectiveness is evaluated using real-life data, and all the parameters needed to determine the basic reproduction number are estimated. Sensitivity analysis is performed to pinpoint the crucial parameters significantly influencing the spread of the infection. The interaction between threshold parameters and the basic reproduction number is simulated. Control theory is employed to devise and evaluate strategies, such as awareness campaigns, advocating condom usage, and deploying rodenticides to reduce the possibility of virus transmission efficiently.
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  • 文章类型: Journal Article
    结核病(TB)仍然是一个重要的全球健康问题,需要有效的控制策略。本文提出了一个数学模型来评估在结核病控制中医用口罩使用和病例检测的比较有效性。该模型被构造为一个常微分方程系统,并结合了结核病动力学的关键方面,包括缓慢快速的进展,医用口罩使用,案例检测,治疗干预措施和有症状和无症状病例之间的区别。结核病控制的一个关键目标是确保复制数量,Rc,如果Rc超过1,则保持低于1以实现结核病消除或持久性。我们的数学分析揭示了当Rc=1表示结核病控制策略的关键节点时,存在跨临界分叉。这些结果证实,病例检测在减少结核病地方性平衡中有症状的个体的地方性人群中的有效性取决于超过临界阈值。此外,我们的模型是使用印度尼西亚每10万人口的结核病年发病率数据进行校准的,印度,莱索托和安哥拉。我们采用了Bootstrap重采样残差方法来评估参数估计值固有的不确定性,从而提供了参数值的全面分布。尽管新发病率呈下降趋势,这四个国家的再现数大于1,表明在有正在进行的结核病控制方案的情况下,结核病病例持续存在.我们将部分秩相关系数与拉丁超立方抽样方法结合使用,对每个国家/地区的每个拟合参数的Rc参数进行全局敏感性分析。我们发现,与病例检测实施相比,医疗面罩的使用对降低Rc更敏感。为了进一步深入了解必要的控制策略,我们制定了最优控制,并研究了我们模型的成本-效果分析,以调查病例检测和使用医用口罩作为控制措施对结核病传播的影响.成本效益分析表明,将这些干预措施结合起来是结核病控制最具成本效益的策略。我们的研究结果强调了医用口罩及其功效以及病例检测在塑造结核病控制动态方面的至关重要性。阐明管理控制再现数的主要参数。我们设想,如果由参与结核病控制工作的政策制定者和医疗保健从业人员实施,我们的发现将对结核病控制产生影响并至关重要。
    Tuberculosis (TB) remains a significant global health concern, necessitating effective control strategies. This article presents a mathematical model to evaluate the comparative effectiveness of medical mask usage and case detection in TB control. The model is constructed as a system of ordinary differential equations and incorporates crucial aspects of TB dynamics, including slow-fast progression, medical mask use, case detection, treatment interventions and differentiation between symptomatic and asymptomatic cases. A key objective of TB control is to ensure that the reproduction number, R c , remains below unity to achieve TB elimination or persistence if R c exceeds 1. Our mathematical analysis reveals the presence of a transcritical bifurcation when the R c = 1 signifies a critical juncture in TB control strategies. These results confirm that the effectiveness of case detection in diminishing the endemic population of symptomatic individuals within a TB-endemic equilibrium depends on exceeding a critical threshold value. Furthermore, our model is calibrated using TB yearly case incidence data per 100 000 population from Indonesia, India, Lesotho and Angola. We employed the bootstrap resampling residual approach to assess the uncertainty inherent in our parameter estimates which provides a comprehensive distribution of the parameter values. Despite a declining trend in new incidence, these four countries exhibit a reproduction number greater than 1, indicating persistent TB cases in the presence of ongoing TB control programmes. We employ the partial rank correlation coefficient in conjunction with the Latin hypercube sampling method to conduct a global sensitivity analysis of the R c parameter for each fitted parameter in every country. We find that the medical mask use is more sensitive to reduce R c compared with the case detection implementation. To further gain insight into the necessary control strategy, we formulated an optimal control and studied the cost-effectiveness analysis of our model to investigate the impact of case detection and medical mask use as control measures in TB spread. Cost-effectiveness analysis demonstrates that combining these interventions emerges as the most cost-effective strategy for TB control. Our findings highlight the critical importance of medical masks and their efficacy coupled with case detection in shaping TB control dynamics, elucidating the primary parameter of concern for managing the control reproduction number. We envisage our findings to have implications and be vital for TB control if implemented by policymakers and healthcare practitioners involved in TB control efforts.
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