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Solving fractional variable-order differential equations of the non-singular derivative using Jacobi operational matrix 利用Jacobi运算矩阵求解非奇异导数的分数阶变阶微分方程
Pub Date : 2023-05-05 DOI: 10.46481/jnsps.2023.1221
M. Basim, N. Senu, A. Ahmadian, Z. Ibrahim, S. Salahshour
This research derives the shifted Jacobi operational matrix (JOM) with respect to fractional derivatives, implemented with the spectral tau method for the numerical solution of the Atangana-Baleanu Caputo (ABC) derivative. The major aspect of this method is that it considerably simplifies problems by reducing them to ones that can be solved by solving a set of algebraic equations. The main advantage of this method is its high robustness and accuracy gained by a small number of Jacobi functions. The suggested approaches are applied in solving non-linear and linear ABC problems according to initial conditions, and the efficiency and applicability of the proposed method are proved by several test examples. A lot of focus is placed on contrasting the numerical outcomes discovered by the new algorithm together with those discovered by previously well-known methods.
本研究导出了关于分数阶导数的移位Jacobi操作矩阵(JOM),并利用谱tau方法实现了Atangana-Baleanu Caputo (ABC)导数的数值解。这种方法的主要方面是,它通过将问题简化为可以通过求解一组代数方程来解决的问题,从而大大简化了问题。该方法的主要优点是鲁棒性和精度高,且使用的雅可比函数较少。将所提方法应用于求解非线性和线性ABC问题,并通过实例验证了所提方法的有效性和适用性。将新算法发现的数值结果与先前已知方法发现的结果进行比较是重点。
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引用次数: 0
A DFT study of optoelectronic, elastic and thermo-electric properties of the double perovskites Rb2SeX6 (X=Br,Cl) 双钙钛矿Rb2SeX6 (X=Br,Cl)的光电、弹性和热电性质的DFT研究
Pub Date : 2023-05-02 DOI: 10.46481/jnsps.2023.1418
Wasiu Yahya, A. A. Yahaya, A. A. Adewale, A. A. Sholagberu, N. Olasunkanmi
Thermo-electric (TE) material applications reduce reliance on traditional energy resources by converting heat to electric energy. We have studied, for the first time, the thermo-electric properties of Rb2SeX6 (X=Br,Cl). Using norm-conserving pseudo potentials in a plane wave basis set of Quantum Espresso code, the optoelectronic, elastic and thermo-electric properties of Rb2SeX6 (X=Br,Cl) have been investigated using density functional theory. Generalized Gradient Approximation of Perdew Burke Ernzerhof (GGA-PBE) and Generalized Gradient Approximation of Perdew Burke Ernzerhof adapted for Solid (GGA-PBESol) exchange correlation functionals were employed in all calculations. The band structure plots suggest that the studied double perovskites have indirect band gaps. Rb2SeBr6 band gap values of 1.7574/ 1.569 eV (using GGA-PBE/PBEsol) are remarkably similar to that of two effective inorganic/organic perovskites FAPbI3 and MAPbI3 . Maximum peaks generated from refractive index results indicate possible solar cell uses of the materials because they are in the visible and ultraviolet ranges. The results of other optical properties such as absorption coefficients, electron energy loss, conductivity, and reflectivity concludes that Rb2SeX6 (X=Br,Cl) have good values for electron generation, high potential for applications in the optoelectronic industry and are semiconductor in nature. The calculated shear anisotropy values of Rb2SeBr6/Cl6 are 3.09/1.71, suggesting that they are isotropic materials. With calculated Poisson’s ratio of 0.32 and 0.26, the materials are predicted to be ductile in nature. The two materials are appropriate for thermo-electric applications since their thermal to electrical conductivity ratio are small (the order of 10-5). The calculated minimum values of Seebeck coefficient values of 0.198×103 / 0.166 ×103 (mV/K) at 750 K, for Rb2SeBr6/Cl6 are positive, indicating that they have p-type conduction. Figure of merit values at all temperature range considered are greater than one (ZT > 1) for both Rb2SeBr6 and Rb2SeCl6, suggesting that they are good thermo-electric materials. The results of the calculations provide the basis for the industrial application of Rb2SeBr6/Cl6 as solar cells.
热电(TE)材料的应用通过将热能转化为电能来减少对传统能源的依赖。我们首次研究了Rb2SeX6 (X=Br,Cl)的热电性质。利用量子Espresso码平面波基集中的保范赝势,利用密度泛函理论研究了Rb2SeX6 (X=Br,Cl)的光电、弹性和热电性质。所有计算均采用Perdew Burke Ernzerhof的广义梯度近似(GGA-PBE)和Perdew Burke Ernzerhof的适用于固体的广义梯度近似(GGA-PBESol)交换相关泛函数。带结构图表明所研究的双钙钛矿具有间接带隙。Rb2SeBr6的带隙值为1.7574/ 1.569 eV(使用GGA-PBE/PBEsol),与两种有效无机/有机钙钛矿FAPbI3和MAPbI3的带隙值非常相似。折射率结果产生的最大峰值表明该材料可能用于太阳能电池,因为它们在可见光和紫外线范围内。其他光学性质,如吸收系数,电子能量损失,电导率和反射率的结果表明,Rb2SeX6 (X=Br,Cl)具有良好的电子生成值,在光电工业中具有很高的应用潜力,并且本质上是半导体。计算得到Rb2SeBr6/Cl6的剪切各向异性值为3.09/1.71,表明它们是各向同性材料。计算得到的泊松比分别为0.32和0.26,预测材料具有延展性。这两种材料适合热电应用,因为它们的导热系数比很小(10-5的数量级)。在750 K时,Rb2SeBr6/Cl6的塞贝克系数值0.198×103 / 0.166 ×103 (mV/K)的最小值为正,表明它们具有p型导电。在考虑的所有温度范围内,Rb2SeBr6和rb2secr6的优点值都大于1 (ZT > 1),表明它们是良好的热电材料。计算结果为Rb2SeBr6/Cl6作为太阳能电池的工业应用提供了依据。
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引用次数: 0
Tuning the optical properties and some surface structure of Cd-O thin film electrodeposited by two-electrode: An effect of Cobalt incorporation 双电极电沉积Cd-O薄膜的光学性能和某些表面结构的调整:钴掺杂的影响
Pub Date : 2023-05-02 DOI: 10.46481/jnsps.2023.1222
R. A. Busari, E. Omotoso, L. Animasahun, S. Adewinbi, E. Adewumi, Comfort T. Famoroti, B. Taleatu, A. Fasasi
The tuning of optical and dielectric parameters, structural and microstructural properties of CdO synthesized via a solution growth two-electrode cell arrangement under ambient environment, with the incorporation of Co ion into its matrix was investigated. The energy band gaps of the films was estimated in the range of 1.69 eV
研究了在环境条件下,采用溶液生长双电极排列法合成的含Co离子的CdO的光学和介电参数的调谐、结构和微观结构性能。薄膜的能带隙在1.69 eV
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引用次数: 0
On Bivariate Nadarajah-Haghighi Distribution derived from Farlie-Gumbel-Morgenstern copula in the Presence of Covariates 存在协变量时由Farlie-Gumbel-Morgenstern联结导出的二元Nadarajah-Haghighi分布
Pub Date : 2023-05-01 DOI: 10.46481/jnsps.2023.871
Yakubu Aliyu, U. Usman
An important alternative distribution to the Weibull, generalized exponen-tial and gamma distributions that is used in survival analysis is the Nadarajah-Haghighi exponential distribution. Similar to the Weibull, generalized exponen-tial and gamma distributions, the Nadarajah-Haghighi exponential distributionis an extension of the well known exponential distribution. In this paper, a copulafunction commonly used to model very weak linear dependence was used to intro-duced a bivariate Nadarajah-Haghighi distribution. The joint survival function,joint probability density function and joint cumulative distribution were givenin closed form. Bayesian method of estimation was used to estimate the modelparameters considering the presence of right censoring and covariates. Posteriorsummaries of interest were obtained via standard Markov Monte Carlo (MCMC )technique. Two real data sets were used to illustrate the importance and flexi-bility of the bivariate model in comparison with some competing models. It wasobserved that, the bivariate Nadarajah-Haghighi distribution provides a better fltthan bivariate exponential, bivariate Weibull, bivariate generalized exponentialand bivariate modified Weibull distributions.
在生存分析中使用的Weibull分布、广义指数分布和gamma分布的一个重要替代分布是Nadarajah-Haghighi指数分布。与Weibull、广义指数分布和gamma分布类似,Nadarajah-Haghighi指数分布是众所周知的指数分布的扩展。本文利用一个通常用于模拟极弱线性依赖的共函数,引入了二元Nadarajah-Haghighi分布。给出了联合生存函数、联合概率密度函数和联合累积分布的封闭形式。考虑右截距和协变量的存在,采用贝叶斯估计方法对模型参数进行估计。通过标准马尔可夫蒙特卡罗(MCMC)技术获得感兴趣的后验摘要。用两个真实的数据集来说明与一些竞争模型相比,二元模型的重要性和灵活性。结果表明,二元Nadarajah-Haghighi分布比二元指数分布、二元威布尔分布、二元广义指数分布和二元修正威布尔分布具有更好的平滑性。
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引用次数: 0
Numerical Simulation of Nonlinear and Non-Isothermal Liquid Chromatography for Studying Thermal Variations in Columns Packed with Core-Shell Particles 非线性非等温液相色谱法研究核壳颗粒填充柱中热变化的数值模拟
Pub Date : 2023-04-24 DOI: 10.46481/jnsps.2023.1350
A. Ahmad, N. F. Okechi, David U. Uche, Abdulwasiu O. Salaudeen
A high-resolution flux-limiting semi-discrete finite volume scheme (HR-FVS) is applied in this study to numerically approximate the nonlinear and non-isothermal flow of one-dimensional lumped kinetic model (1D-LKM), for a fixed-bed column loaded with core-shell particles. The developed model comprise a system of convection-dominated partial differential for mass and energy balances in the mobile phases coupled with differential equation and algebraic equation in the stationary phase. The solution of the model equations is obtained by utilizing a HR-FVS, the scheme has second-order accuracy even on the grid coarse and its explicit nature has the potential to resolve the arisen sharp discontinuities in the solution profiles. A second-order total variation diminishing (TVD) Runge-Kutta technique is used to solve the system of ODEs in time. Several forms of a single-solute mixture are produced to investigate the influences of the fractions of core radius on thermal waves and concentration fronts. Moreover, a particular criterion is introduced for analyzing the performance of the underlying process and to identify the optimal parameter values of the fraction of core radius.
本文采用高分辨率限流半离散有限体积格式(HR-FVS),对含核壳颗粒的固定床柱的一维集总动力学模型(1D-LKM)的非线性非等温流动进行了数值模拟。所建立的模型包括流动相中以对流为主的质量和能量平衡偏微分系统,以及固定相中的微分方程和代数方程。利用HR-FVS获得模型方程的解,该方案即使在粗糙网格上也具有二阶精度,其显式性质具有解决解剖面中出现的尖锐不连续的潜力。采用二阶全变差递减(TVD)龙格-库塔技术及时求解ode系统。制备了几种形式的单溶质混合物,以研究岩心半径分数对热波和浓度锋的影响。此外,还引入了一个特定的准则来分析底层过程的性能,并确定岩心半径分数的最佳参数值。
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引用次数: 0
An integral approach for complete migration from a relational database to MongoDB 从关系数据库完全迁移到MongoDB的集成方法
Pub Date : 2023-04-24 DOI: 10.46481/jnsps.2023.1089
Abdelhak Erraji, A. Maizate, M. Ouzzif
Today, computing has become an obligation in the lives of individuals and institutions alike. This magical sector uses and develops very rich, important, and sensitive tools and solutions, which make everyone's life easier. Computers with their tools have become indispensable and they have transformed the world into a small town. These tools revolve around data, the type, nature, and size of which continually increases up to zeta bytes of storage capacity, thus creating BigData. Considering that Relational databases present difficulties in the management of BigData, and Knowing that companies want to keep their data accumulated over decades of exercises and studies on the market, and also taking into account the cost impact if they kept both systems in terms of software, technical support and user training; therefore it is legitimate to find a reliable way to migrate their data from the relational system to a NoSQL system, which designed specifically to handle BigData. In this optic, several studies and approaches have been developed, but they present a lack or weaknesses in the treatment of the main components of the database, which we are going to deal with in our new and integrated approach to migration from the relational database system to MongoDB as a NoSQL system. In this article, we will present our contribution by developing a complete concept of our approach, starting with an introduction, which will be followed by a discussion of what other researchers have done in this direction, then we move on to a phase of analysis and modeling to develop the models and meta-models of the two systems: source and destination, also during this section we also present our analysis and modeling methodology, to present our global approach which divides its treatment into three axes, each of which processes a part of the RDBMS with a particular nature of data: data stored in tables, data carried on the structure of the RDBMS and data coming from the semantics of relational databases. The overall architecture of our approach, which we named ''TMSDRDND'', is formed by two layers: ''TSRSNLayer'' which deals with the transformation of the structure and the transfer of semantic data, and the ''MDRSNLayer'' layer, Which takes care of data migration using an ETL to be developed according to a specific concept and architecture and exploiting the results of the first layer.
今天,计算已经成为个人和机构生活中的一种义务。这个神奇的部门使用和开发非常丰富、重要和敏感的工具和解决方案,使每个人的生活更轻松。计算机和它们的工具已经变得不可或缺,它们把世界变成了一个小镇。这些工具围绕着数据,数据的类型、性质和大小不断增加到zeta字节的存储容量,从而创建了大数据。考虑到关系型数据库在管理大数据方面存在困难,公司希望保留其在市场上几十年的实践和研究积累的数据,同时考虑到如果同时保留这两个系统在软件、技术支持和用户培训方面的成本影响;因此,找到一种可靠的方法将他们的数据从关系系统迁移到NoSQL系统是合理的,NoSQL系统是专门为处理大数据而设计的。从这个角度来看,已经开发了一些研究和方法,但它们在处理数据库的主要组件方面存在不足或弱点,我们将在从关系数据库系统迁移到MongoDB作为NoSQL系统的新的集成方法中处理这些问题。在本文中,我们将通过开发我们方法的完整概念来展示我们的贡献,从介绍开始,然后讨论其他研究人员在这个方向上所做的工作,然后我们进入分析和建模阶段,以开发两个系统的模型和元模型:在本节中,我们还将介绍我们的分析和建模方法,以展示我们的全局方法,该方法将其处理分为三个轴,每个轴处理RDBMS中具有特定数据性质的一部分:存储在表中的数据,RDBMS结构上携带的数据和来自关系数据库语义的数据。我们命名为“TMSDRDND”的方法的整体架构由两层组成:“TSRSNLayer”处理结构转换和语义数据的传输,“MDRSNLayer”层处理数据迁移,使用根据特定概念和架构开发的ETL并利用第一层的结果。
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引用次数: 0
Solar Energy Storage by Fuel Cell Technology at Abomey-Calavi (Benin) Abomey-Calavi(贝宁)的燃料电池太阳能存储技术
Pub Date : 2023-04-22 DOI: 10.46481/jnsps.2023.1264
Odilon Joseph Towanou, H. Donnou, G. K. N'Gobi, Augustin Enonsi Leode, Basile Kounouh´ewa
West Africa has a great amount of sunshine power, varying between 5 kWh.m^{-2}.day^{-1} and 7 kWh.m^{-2}.day^{-1}. This power constitutes high energy source in the region. However, several locations in that area have no access to energy because of the lack of suitable technology and projects exploiting the source. The fundamental problem related to sun power or to renewable energies in general is the lack of efficient technology for energy storage. Batteries are generally used for this storage, but once charged, the excess of the energy from the solar photovoltaic panels (PV) is lost. Therefore, it is very important to find a system to recover the excess in order to optimize its use. In this context, hydrogen is considered a very promising candidate to fulfill this function and could become a highly developed energy vector in the future. The very numerous works undertaken over the past decade for the production of electricity by hydrogen fuel cells bear witness to this. The objective of this study is to test a more reliable solar energy storage system by using fuel cell technology. To achieve this, three steps have been necessary: (i) make an electrolyser using materials, (ii) produce hydrogen using a system of PV panels and (iii) convert the hydrogen produced into electricity through a fuel cell. The results obtained indicate a production of 0.020 m^3 of hydrogen after 150 min with a yield of 85.86%. The production of electricity by a 2 V fuel cell gives an efficiency of 0.0042%. Even if this value is low, a part of the lost energy has been recovered. In view of these results, the improvement of the device for converting chemical energy into electricity deserves to be deeply explored in West Africa.
西非有大量的太阳能,在5千瓦时m^{-2}之间变化。day^{-1}和7kwh .m^{-2}.day^{-1}。这种电力构成了该地区的高能量来源。然而,由于缺乏适当的技术和开发能源的项目,该地区的几个地点无法获得能源。与太阳能或一般可再生能源有关的根本问题是缺乏有效的能源储存技术。电池通常用于这种存储,但是一旦充电,太阳能光伏板(PV)的多余能量就会丢失。因此,找到一个系统来回收多余的水,以优化其使用是非常重要的。在这种情况下,氢被认为是实现这一功能的非常有前途的候选者,并可能在未来成为一种高度发达的能量载体。在过去的十年中,通过氢燃料电池发电的大量工作证明了这一点。本研究的目的是通过使用燃料电池技术来测试一个更可靠的太阳能存储系统。为了实现这一目标,需要三个步骤:(1)使用材料制造电解槽,(2)使用光伏板系统产生氢气,(3)通过燃料电池将产生的氢气转化为电能。结果表明,反应150 min后,产氢量为0.020 m^3,产率为85.86%。2伏燃料电池的发电效率为0.0042%。即使这个值很低,也有一部分损失的能量被恢复了。鉴于这些结果,改进将化学能转化为电能的装置值得在西非进行深入探索。
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引用次数: 0
An Empirical Study on Anomaly Detection Using Density-based and Representative-based Clustering Algorithms 基于密度和代表性聚类算法的异常检测实证研究
Pub Date : 2023-04-19 DOI: 10.46481/jnsps.2023.1364
Gerard Shu Fuhnwi, Janet O. Agbaje, K. Oshinubi, O. J. Peter
In data mining, and statistics, anomaly detection is the process of finding data patterns (outcomes, values, or observations) that deviate from the rest of the other observations or outcomes. Anomaly detection is heavily used in solving real-world problems in many application domains, like medicine, finance , cybersecurity, banking, networking, transportation, and military surveillance for enemy activities, but not limited to only these fields. In this paper, we present an empirical study on unsupervised anomaly detection techniques such as Density-Based Spatial Clustering of Applications with Noise (DBSCAN), (DBSCAN++) (with uniform initialization, k-center initialization, uniform with approximate neighbor initialization, and $k$-center with approximate neighbor initialization), and $k$-means$--$ algorithms on six benchmark imbalanced data sets. Findings from our in-depth empirical study show that k-means-- is more robust than DBSCAN, and DBSCAN++, in terms of the different evaluation measures (F1-score, False alarm rate, Adjusted rand index, and Jaccard coefficient), and running time. We also observe that DBSCAN performs very well on data sets with fewer number of data points. Moreover, the results indicate that the choice of clustering algorithm can significantly impact the performance of anomaly detection and that the performance of different algorithms varies depending on the characteristics of the data. Overall, this study provides insights into the strengths and limitations of different clustering algorithms for anomaly detection and can help guide the selection of appropriate algorithms for specific applications.
在数据挖掘和统计中,异常检测是查找偏离其他观察值或结果的数据模式(结果、值或观察值)的过程。异常检测在许多应用领域被大量用于解决现实世界的问题,如医学、金融、网络安全、银行、网络、交通和军事监视敌人的活动,但不仅限于这些领域。在本文中,我们在六个基准不平衡数据集上对无监督异常检测技术进行了实证研究,如基于密度的带噪声应用空间聚类(DBSCAN)、(DBSCAN++)(均匀初始化、k中心初始化、均匀与近似邻居初始化、$k$-中心与近似邻居初始化)和$k$-means$- $算法。通过深入的实证研究发现,在不同的评价指标(f1得分、虚警率、调整后的rand指数和Jaccard系数)和运行时间方面,k-means-比DBSCAN和DBSCAN++更具鲁棒性。我们还观察到,DBSCAN在数据点数量较少的数据集上执行得非常好。此外,结果表明,聚类算法的选择会显著影响异常检测的性能,不同算法的性能取决于数据的特征。总的来说,本研究提供了不同的聚类算法异常检测的优势和局限性的见解,可以帮助指导为特定应用选择合适的算法。
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引用次数: 2
Annual Effective Dose and Excess Lifetime Cancer Risk due to Ingestion and Inhalation of Radon in Groundwater of Bosso Community Minna, North-Central Nigeria 尼日利亚中北部米纳博索社区地下水中氡的年有效剂量和过量终生癌症风险
Pub Date : 2023-04-19 DOI: 10.46481/jnsps.2023.896
M. Kolo, O. Olarinoye, S. Salihu, Hyginus Anayo Ugwuanyi, P. Onuche, Opeyemi Falade, Nwachukwu Chibueze
Radon in potable water has become an issue of public health concern, especially when consumed or used directly from source for domestic purposes without any pre-treatment. In this study, 222Rn concentration in 22 water samples collected from 2 groundwater sources (open wells, 12 samples and boreholes, 10 samples) in Bosso town, North central Nigeria were measured using Durridge RAD-7 radon detector with RAD-H2O accessories. 222Rn concentrations in open wells varied from 2.1±0.7 to 27.9±2.5 Bq L-1 with a mean of 10.2±1.5 Bq L-1, while that in boreholes ranged from 2.8±1.1 to 39.2±1.5 Bq L-1 with a mean value of 14.3±1.7 Bq L-1. These values are lower than the 100 Bq L-1 upper limit proposed by the European Union Commission, above which any practical intervention may be necessary. Mean annual committed effective dose to adults, children and infants from ingestion of water were 74.64, 71.58 and 53.17 muSv y-1 respectively for the open wells and 104.24, 99.96 and 74.26 muSv y-1 respectively for borehole water samples. Mean whole body dose due to ingestion and inhalation of waterborne radon from open wells and boreholes are 27.56 and 38.48 muSv y-1 respectively, which are below the reference level of 0.1 mSv y-1 for potable water recommended by the World Health Organization for public safety. The excess lifetime cancer risk were 0.10 × 10-3 for the open wells and 0.13 × 10-3 for the boreholes, which are lower than the world safety limit 0.29 × 10-3. Water from the two groundwater sources investigated is therefore fit for consumption and other domestic usage from the point of view of radiation protection.   
饮用水中的氡已成为一个令人关注的公共卫生问题,特别是在未经任何预处理的情况下饮用或直接从源头用于家庭用途。本研究采用带有RAD-H2O附件的Durridge RAD-7型氡探测器,对尼日利亚中北部博索镇2个地下水源(露天井12个,钻孔10个)采集的22个水样中的222Rn浓度进行了测定。裸井222Rn浓度变化范围为2.1±0.7 ~ 27.9±2.5 Bq L-1,平均值为10.2±1.5 Bq L-1;钻孔222Rn浓度变化范围为2.8±1.1 ~ 39.2±1.5 Bq L-1,平均值为14.3±1.7 Bq L-1。这些数值低于欧盟委员会建议的100 Bq L-1上限,超过该上限可能需要任何实际干预。裸井饮水对成人、儿童和婴儿的年平均承诺有效剂量分别为74.64、71.58和53.17 μ v -1,钻孔饮水对成人、儿童和婴儿的年平均承诺有效剂量分别为104.24、99.96和74.26 μ v -1。从露天井和钻孔中摄入和吸入水源性氡的平均全身剂量分别为27.56毫西弗-1和38.48毫西弗-1,低于世界卫生组织为公共安全建议的饮用水参考水平0.1毫西弗-1。裸井和钻孔的终生癌症风险分别为0.10 × 10-3和0.13 × 10-3,均低于世界安全限值0.29 × 10-3。因此,从辐射防护的角度来看,所调查的两个地下水源的水适合用于消费和其他家庭用途。
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引用次数: 0
Understanding the Transmission Dynamics and Control of HIV Infection: A Mathematical Model Approach 理解HIV感染的传播动力学和控制:一种数学模型方法
Pub Date : 2023-04-19 DOI: 10.46481/jnsps.2023.1389
Saheed Ajao, I. Olopade, T. Akinwumi, S. Adewale, A. Adesanya
New challenges like the outbreak of new diseases, government policies, war and insurgency etc. present distortion, delay and denial of persons’ access to ART, thereby fuelling the spread and increasing the burden of HIV/AIDS. A mathematical model is presented to study the transmission dynamics and control of HIV infection. The qualitative and quantitative analyses of the model are carried out. It is shown that the disease-free equilibrium of the model is globally asymptotically stable whenever the basic reproduction number is less than unity. It is also shown that a unique endemic equilibrium exists whenever the basic reproduction number exceeds unity and that the model exhibits a forward bifurcation. Furthermore, the Lyapunov function is used to show that the endemic equilibrium is globally asymptotically stable for a special case of the model whenever the associated basic reproduction number is greater than unity. The model is calibrated to the data on HIV/AIDS prevalence in Nigeria from 1990 to 2019 and it represents reality. The numerical simulations on the global stability of disease-free equilibrium and endemic equilibrium justify the analytic results. The fraction of the detected individuals who stays in the treatment class plays a significant role as it influences the population of the latently-infected individuals and AIDS class by preventing individuals from progressing into the AIDS class.
新的挑战,如新疾病的爆发、政府政策、战争和叛乱等,造成扭曲、拖延和拒绝人们获得抗逆转录病毒治疗,从而助长了艾滋病毒/艾滋病的蔓延并增加了其负担。提出了一个研究HIV感染传播动力学和控制的数学模型。对模型进行了定性和定量分析。证明了当基本繁殖数小于1时,该模型的无病平衡点是全局渐近稳定的。结果表明,当基本繁殖数超过1时,存在唯一的地方性平衡,模型呈现正向分岔。进一步,利用Lyapunov函数证明了当相关的基本繁殖数大于1时,模型的局部平衡点是全局渐近稳定的。该模型是根据尼日利亚1990年至2019年艾滋病毒/艾滋病流行率的数据进行校准的,它代表了现实。对无病平衡和地方病平衡的全局稳定性进行了数值模拟,验证了分析结果。检测到的个体中留在治疗组的比例发挥着重要作用,因为它通过阻止个体进入艾滋病组而影响潜在感染个体和艾滋病组的人口。
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Journal of the Nigerian Society of Physical Sciences
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