In this study, we applied an approximate solution method for solving the boundary value problems (BVPs) with retarded argument. The method is the consecutive substitution method. The consecutive substitution method was applied and an approximate solution was obtained. The numerical solution and the analytical solution are compared in the table. The solutions were found to be compatible.
{"title":"The Consecutive Substitution Method for Boundary Value Problems (BVPs) with Retarded Argument","authors":"A. Aykut, E. Çelik","doi":"10.1155/2023/3226604","DOIUrl":"https://doi.org/10.1155/2023/3226604","url":null,"abstract":"In this study, we applied an approximate solution method for solving the boundary value problems (BVPs) with retarded argument. The method is the consecutive substitution method. The consecutive substitution method was applied and an approximate solution was obtained. The numerical solution and the analytical solution are compared in the table. The solutions were found to be compatible.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"151 1","pages":"3226604:1-3226604:5"},"PeriodicalIF":0.0,"publicationDate":"2023-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74851620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A country’s economic development relies on different features such as export/import, industrial processes, and tourism. Rural tourism is a discussion-centric research field for analyzing its contribution to a country’s economic growth. This field generates voluptuous data for tourists, expenditure, location, etc. analysis; the information increases over the years and the density of visiting tourists. Therefore, this article introduces an optimized reinforcement data analysis approach (ORDAA) for generating precise guidance information. This information is two-faced, namely, summarized data for tourist guidance and summarized data for the country’s economic development. Data augmentation’s steep rise and downfall are analyzed using reinforcement learning, wherein decision agents are precise for a relevant summary. The relevance is identified using associated development targets over varying years. Besides, the guidance information that identifies low tourist summary or nonachievable development targets is separately identified. The identified targets are analyzed using reinforcement agents for economic growth improvements compared to the previous tourist densities. This improves the focus on rural tourism sights and economic contributions to an optimal level.
{"title":"Optimized Reinforcement Learning Approach on Sustainable Rural Tourism Development for Economic Growth","authors":"Guofang Chen","doi":"10.1155/2023/4991438","DOIUrl":"https://doi.org/10.1155/2023/4991438","url":null,"abstract":"A country’s economic development relies on different features such as export/import, industrial processes, and tourism. Rural tourism is a discussion-centric research field for analyzing its contribution to a country’s economic growth. This field generates voluptuous data for tourists, expenditure, location, etc. analysis; the information increases over the years and the density of visiting tourists. Therefore, this article introduces an optimized reinforcement data analysis approach (ORDAA) for generating precise guidance information. This information is two-faced, namely, summarized data for tourist guidance and summarized data for the country’s economic development. Data augmentation’s steep rise and downfall are analyzed using reinforcement learning, wherein decision agents are precise for a relevant summary. The relevance is identified using associated development targets over varying years. Besides, the guidance information that identifies low tourist summary or nonachievable development targets is separately identified. The identified targets are analyzed using reinforcement agents for economic growth improvements compared to the previous tourist densities. This improves the focus on rural tourism sights and economic contributions to an optimal level.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"20 1","pages":"4991438:1-4991438:16"},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91302302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we introduce a new generalized inverse, called the G-MPCEP inverse of a complex matrix. We investigate some characterizations, representations, and properties of this new inverse. Cramer’s rule for the solution of a singular equation A x = B is also presented. Moreover, the determinantal representations for the G-MPCEP inverse are studied. Finally, the G-MPCEP inverse being used in solving appropriate systems of linear equations is established.
本文引入了一种新的广义逆，称为复矩阵的G-MPCEP逆。我们研究了这个新逆的一些表征、表示和性质。给出了求解奇异方程a x = B的Cramer规则。此外，还研究了G-MPCEP逆的行列式表示。最后，建立了G-MPCEP逆函数用于求解合适的线性方程组。
{"title":"Characterizations of the Generalized MPCEP Inverse of Rectangular Matrices","authors":"Jiaxuan Yao, Xiaoji Liu, Hongwei Jin","doi":"10.1155/2023/6235312","DOIUrl":"https://doi.org/10.1155/2023/6235312","url":null,"abstract":"In this paper, we introduce a new generalized inverse, called the G-MPCEP inverse of a complex matrix. We investigate some characterizations, representations, and properties of this new inverse. Cramer’s rule for the solution of a singular equation \u0000 \u0000 A\u0000 x\u0000 =\u0000 B\u0000 \u0000 is also presented. Moreover, the determinantal representations for the G-MPCEP inverse are studied. Finally, the G-MPCEP inverse being used in solving appropriate systems of linear equations is established.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"113 1","pages":"6235312:1-6235312:10"},"PeriodicalIF":0.0,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80456359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In order to consider the effect of anisotropy of soil around the pile on the lateral vibration of pile groups, the soil around the pile is regarded as a transversely isotropic medium, and a lateral dynamic interaction model of pile-pile in transversely isotropic soil is established. According to Novak’s plane assumption and wave propagation theory, the lateral vibration of transversely isotropic soil layer is solved by introducing potential function and using mathematical and physical means, and the attenuation function of lateral displacement of free field is given. The Dobry and Dazetas simplified solution of attenuation function is different from that of solution of plane model. The pile-pile horizontal dynamic interaction factor in transversely isotropic soil is obtained by using the initial parameter method and Krylov function. The horizontal dynamic impedance of pile groups is obtained by using the pile-pile superposition principle. The change rule of the lateral displacement attenuation function of transversely isotropic soil with frequency is related to the direction and frequency. The ratio G h v of the shear modulus in the lateral plane to the shear modulus in the vertical plane and the pile spacing S / d have a great impact on the lateral vibration of pile groups, and when the pile spacing is large, the curves of attenuation function varying with frequency fluctuate greatly. The ratio of elastic modulus of pile to vertical plane shear modulus of soil E p / G v has an effect on the lateral stiffness of pile groups, which is related to frequency, while the effect on dynamic damping is not affected by frequency. The difference of mechanical properties on different surfaces of soil around the pile has a great influence on the lateral vibration of pile groups in transversely isotropic soil, and the influence of the anisotropy on the attenuation function of the lateral displacement and the dynamic impedance cannot be ignored.
为考虑桩周土体各向异性对群桩横向振动的影响，将桩周土体视为横向各向同性介质，建立了横向各向同性土体中桩-桩横向动力相互作用模型。根据Novak的平面假设和波传播理论，引入势函数，运用数学和物理手段求解了横观各向同性土层的横向振动，给出了自由场横向位移的衰减函数。衰减函数的Dobry和Dazetas简化解不同于平面模型的解。采用初始参数法和Krylov函数，得到了横向各向同性土中桩-桩水平动力相互作用系数。利用桩-桩叠加原理，得到了群桩的水平动力阻抗。横向各向同性土的侧向位移衰减函数随频率的变化规律与方向和频率有关。横向剪切模量与竖向剪切模量之比G h v和桩间距S / d对群桩横向振动有较大影响，当桩间距较大时，衰减函数随频率变化曲线波动较大。桩弹性模量与土体竖向剪切模量之比exp / gv对群桩侧移刚度的影响与频率有关，而对动力阻尼的影响不受频率的影响。在横向各向同性土体中，桩周不同土体表面的力学特性差异对群桩的横向振动有很大影响，各向异性对横向位移衰减函数和动力阻抗的影响不容忽视。
{"title":"Study on the Lateral Dynamic Impedance of Pile Groups in Transversely Isotropic Soil Using Novak's Plane Model","authors":"Linchao Liu, Qifang Yan","doi":"10.1155/2023/9132285","DOIUrl":"https://doi.org/10.1155/2023/9132285","url":null,"abstract":"In order to consider the effect of anisotropy of soil around the pile on the lateral vibration of pile groups, the soil around the pile is regarded as a transversely isotropic medium, and a lateral dynamic interaction model of pile-pile in transversely isotropic soil is established. According to Novak’s plane assumption and wave propagation theory, the lateral vibration of transversely isotropic soil layer is solved by introducing potential function and using mathematical and physical means, and the attenuation function of lateral displacement of free field is given. The Dobry and Dazetas simplified solution of attenuation function is different from that of solution of plane model. The pile-pile horizontal dynamic interaction factor in transversely isotropic soil is obtained by using the initial parameter method and Krylov function. The horizontal dynamic impedance of pile groups is obtained by using the pile-pile superposition principle. The change rule of the lateral displacement attenuation function of transversely isotropic soil with frequency is related to the direction and frequency. The ratio \u0000 \u0000 \u0000 \u0000 G\u0000 \u0000 \u0000 h\u0000 v\u0000 \u0000 \u0000 \u0000 of the shear modulus in the lateral plane to the shear modulus in the vertical plane and the pile spacing \u0000 \u0000 S\u0000 /\u0000 d\u0000 \u0000 have a great impact on the lateral vibration of pile groups, and when the pile spacing is large, the curves of attenuation function varying with frequency fluctuate greatly. The ratio of elastic modulus of pile to vertical plane shear modulus of soil \u0000 \u0000 \u0000 \u0000 E\u0000 \u0000 \u0000 p\u0000 \u0000 \u0000 /\u0000 \u0000 \u0000 G\u0000 \u0000 \u0000 v\u0000 \u0000 \u0000 \u0000 has an effect on the lateral stiffness of pile groups, which is related to frequency, while the effect on dynamic damping is not affected by frequency. The difference of mechanical properties on different surfaces of soil around the pile has a great influence on the lateral vibration of pile groups in transversely isotropic soil, and the influence of the anisotropy on the attenuation function of the lateral displacement and the dynamic impedance cannot be ignored.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"65 1","pages":"9132285:1-9132285:13"},"PeriodicalIF":0.0,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85789948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Conventionally, the problem of studying the transport of water, heat, and solute in soil or groundwater systems has been numerically solved using finite difference (FD) or finite element (FE) methods. FE methods are attractive over FD methods because they are geometrically flexible. However, recent studies demonstrate that spectral collocation (SC) methods converge exponentially faster than FD or FE methods using a few grid points or on coarse grids. This work proposes and applies a multivariate spectral local quasilinearization method (MV-SLQLM) to model the transportation and interaction of soil moisture, heat, and solute concentration in a nonbare soil ridge. The MV-SLQLM uses a quasilinearization method (QLM) to linearize any nonlinear equations and then employs a local linearization method (LLM) to decouple the linearized system of PDEs to form a sequence of equations that are solved in a computationally efficient manner. The MV-SLQLM is thus an extension of the bivariate spectral local linearization method (BI-SLLM) that fails to deal with a 2D problem and is a modification of the MV-SQLM whose efficiency is compromised when operating on high dense solution matrices. We use the residual error norms of the difference between successive iterations to affirm convergence to the expected solution. To illustrate the application and check the solution accuracy, we conduct systematic analyses of the effect of model parameters on distribution profiles. Findings are in good agreement with theory and literature, thereby revealing suitability of the MV-SLQLM to solve coupled nonlinear PDEs with environmental fluid dynamics applications.
{"title":"A Novel Multivariate Spectral Local Quasilinearization Method (MV-SLQLM) for Modelling Flow, Moisture, Heat, and Solute Transport in Soil","authors":"Elias Mwakilama, V. Magagula, D. Gathungu","doi":"10.1155/2023/7104852","DOIUrl":"https://doi.org/10.1155/2023/7104852","url":null,"abstract":"Conventionally, the problem of studying the transport of water, heat, and solute in soil or groundwater systems has been numerically solved using finite difference (FD) or finite element (FE) methods. FE methods are attractive over FD methods because they are geometrically flexible. However, recent studies demonstrate that spectral collocation (SC) methods converge exponentially faster than FD or FE methods using a few grid points or on coarse grids. This work proposes and applies a multivariate spectral local quasilinearization method (MV-SLQLM) to model the transportation and interaction of soil moisture, heat, and solute concentration in a nonbare soil ridge. The MV-SLQLM uses a quasilinearization method (QLM) to linearize any nonlinear equations and then employs a local linearization method (LLM) to decouple the linearized system of PDEs to form a sequence of equations that are solved in a computationally efficient manner. The MV-SLQLM is thus an extension of the bivariate spectral local linearization method (BI-SLLM) that fails to deal with a 2D problem and is a modification of the MV-SQLM whose efficiency is compromised when operating on high dense solution matrices. We use the residual error norms of the difference between successive iterations to affirm convergence to the expected solution. To illustrate the application and check the solution accuracy, we conduct systematic analyses of the effect of model parameters on distribution profiles. Findings are in good agreement with theory and literature, thereby revealing suitability of the MV-SLQLM to solve coupled nonlinear PDEs with environmental fluid dynamics applications.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"6 1","pages":"7104852:1-7104852:32"},"PeriodicalIF":0.0,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87807506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A numerical investigation is carried out to analyze the impacts of internal heat source size, solid concentration of nanoparticles, magnetic field, and Richardson number on flow characteristics in an oppositely directed lid-driven wavy-shaped enclosure. The left and right vertical walls of the enclosure are cooled isothermally and moving with fixed velocity in upward and downward directions, respectively. The bottom wall is wavy shaped and isothermally cooled as the vertical walls while the top wall is kept adiabatic. A rectangular heater is placed horizontally in the center of the cavity. The physical problems are characterized by 2D governing partial differential equations accompanying proper boundary conditions and are discretized using Galerkin’s finite element formulation. The study is executed by analyzing different ranges of geometrical and physical parameters, namely, internal heat source length 0.2 ≤ CH ≤ 0.6 , solid concentration of nanoparticles 0 ≤ φ ≤ 0.09 , Hartmann’s number 0 ≤ Ha ≤ 70 , and Richardson’s number 0.1 ≤ Ri ≤ 10 . The results indicate that the overall heat transfer rate declines with the increasing length of internal heat source. The presence and rising values of solid concentration of nanoparticles cause the augmentation of heat transfer whereas the magnetic field has a negative influence and the Richardson number has a positive influence on heat transfer.
{"title":"Mixed Convection in a Double Lid-Driven Wavy Shaped Cavity Filled with Nanofluid Subject to Magnetic Field and Internal Heat Source","authors":"Kakali Chowdhury, M. A. Alim","doi":"10.1155/2023/7117186","DOIUrl":"https://doi.org/10.1155/2023/7117186","url":null,"abstract":"A numerical investigation is carried out to analyze the impacts of internal heat source size, solid concentration of nanoparticles, magnetic field, and Richardson number on flow characteristics in an oppositely directed lid-driven wavy-shaped enclosure. The left and right vertical walls of the enclosure are cooled isothermally and moving with fixed velocity in upward and downward directions, respectively. The bottom wall is wavy shaped and isothermally cooled as the vertical walls while the top wall is kept adiabatic. A rectangular heater is placed horizontally in the center of the cavity. The physical problems are characterized by 2D governing partial differential equations accompanying proper boundary conditions and are discretized using Galerkin’s finite element formulation. The study is executed by analyzing different ranges of geometrical and physical parameters, namely, internal heat source length \u0000 \u0000 \u0000 \u0000 0.2\u0000 ≤\u0000 CH\u0000 ≤\u0000 0.6\u0000 \u0000 \u0000 \u0000 , solid concentration of nanoparticles \u0000 \u0000 \u0000 \u0000 0\u0000 ≤\u0000 φ\u0000 ≤\u0000 0.09\u0000 \u0000 \u0000 \u0000 , Hartmann’s number \u0000 \u0000 \u0000 \u0000 0\u0000 ≤\u0000 Ha\u0000 ≤\u0000 70\u0000 \u0000 \u0000 \u0000 , and Richardson’s number \u0000 \u0000 \u0000 \u0000 0.1\u0000 ≤\u0000 Ri\u0000 ≤\u0000 10\u0000 \u0000 \u0000 \u0000 . The results indicate that the overall heat transfer rate declines with the increasing length of internal heat source. The presence and rising values of solid concentration of nanoparticles cause the augmentation of heat transfer whereas the magnetic field has a negative influence and the Richardson number has a positive influence on heat transfer.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"103 1 1","pages":"7117186:1-7117186:13"},"PeriodicalIF":0.0,"publicationDate":"2023-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85573122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we utilized a hybrid method for the unsteady flow of the non-Newtonian third-grade fluid that combines the finite difference with the asymptotic interpolation method. This hybrid method is used to satisfy the semiunbound domain condition of the fluid flow’s length approaching infinity. The primary issue with this research is how much of the hybrid approach’s error may be accepted to guarantee that the method is significant. This paper discussed theoretical error analysis for numerical solutions, including the range and norm of error. The perturbation method’s concept is used to assess the hybrid method’s error. It is discovered that the hybrid approach’s relative error norm is lower than that of the finite difference method. In terms of the error standard, the hybrid approach is more consistent. Error analysis is performed to check for the accuracy as well as the platform for variable mesh size finite difference method in the future research.
{"title":"Theoretical Error Analysis of Hybrid Finite Difference-Asymptotic Interpolation Method for Non-Newtonian Fluid Flow","authors":"S. Mahadi, S. Yeak, N. Arbin, F. Salah","doi":"10.1155/2023/9920157","DOIUrl":"https://doi.org/10.1155/2023/9920157","url":null,"abstract":"In this paper, we utilized a hybrid method for the unsteady flow of the non-Newtonian third-grade fluid that combines the finite difference with the asymptotic interpolation method. This hybrid method is used to satisfy the semiunbound domain condition of the fluid flow’s length approaching infinity. The primary issue with this research is how much of the hybrid approach’s error may be accepted to guarantee that the method is significant. This paper discussed theoretical error analysis for numerical solutions, including the range and norm of error. The perturbation method’s concept is used to assess the hybrid method’s error. It is discovered that the hybrid approach’s relative error norm is lower than that of the finite difference method. In terms of the error standard, the hybrid approach is more consistent. Error analysis is performed to check for the accuracy as well as the platform for variable mesh size finite difference method in the future research.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"16 1","pages":"9920157:1-9920157:9"},"PeriodicalIF":0.0,"publicationDate":"2023-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87433422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fenhong Li, Zaisheng Wang, Chongan Pang, Hai-Xi Yang
The objective of this paper is to study the antidamage ability of beam column joints in complex steel structures under external forces and to improve the safety of such structures. In this study, a three-dimensional model of complex steel structure based on BIM technology is proposed by analyzing and calculating the ultimate strength of complex steel structure for mine protection. The vibration control algorithm of complex steel structure for mine protection is designed, and the boundary elastic constraint conditions are determined. According to the constraint conditions, the vibration characteristics of complex steel structures for mining are analyzed. The experimental results show that the maximum displacement of the design model is reduced by half compared with that before optimization, which can meet the design requirements.
{"title":"3D Modeling of Mine Protection Complex Steel Structure Based on BIM Technology","authors":"Fenhong Li, Zaisheng Wang, Chongan Pang, Hai-Xi Yang","doi":"10.1155/2023/7193935","DOIUrl":"https://doi.org/10.1155/2023/7193935","url":null,"abstract":"The objective of this paper is to study the antidamage ability of beam column joints in complex steel structures under external forces and to improve the safety of such structures. In this study, a three-dimensional model of complex steel structure based on BIM technology is proposed by analyzing and calculating the ultimate strength of complex steel structure for mine protection. The vibration control algorithm of complex steel structure for mine protection is designed, and the boundary elastic constraint conditions are determined. According to the constraint conditions, the vibration characteristics of complex steel structures for mining are analyzed. The experimental results show that the maximum displacement of the design model is reduced by half compared with that before optimization, which can meet the design requirements.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"31 1","pages":"7193935:1-7193935:9"},"PeriodicalIF":0.0,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87817193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, a nonlinear deterministic mathematical model that evaluates two important therapeutic measures of the COVID-19 pandemic: vaccination of susceptible and treatment for infected people who are in quarantine, is formulated and rigorously analyzed. Some of the fundamental properties of the model system including existence and uniqueness, positivity, and invariant region of solutions are proved under a certain meaningful set. The model exhibits two equilibrium points: disease-free and endemic equilibrium points under certain conditions. The basic reproduction number, R 0 , is derived via the next-generation matrix approach, and the dynamical behavior of the model is explored in detail. The analytical analysis reveals that the disease-free equilibrium solution is locally as well as globally asymptotically stable when the associated basic reproduction number is less than unity which indicates that COVID-19 dies out in the population. Also, the endemic equilibrium point is globally asymptotically stable whenever the associated basic reproduction number exceeds a unity which implies that COVID-19 establishes itself in the population. The sensitivity analysis of the basic reproduction number is computed to identify the most dominant parameters for the spreading out as well as control of infection and should be targeted by intervention strategies. Furthermore, we extended the considered model to optimal control problem system by introducing two time-dependent variables that represent the educational campaign to susceptibles and continuous treatment for quarantined individuals. Finally, some numerical results are illustrated to supplement the analytical results of the model using MATLAB ode45.
{"title":"Mathematical Model and Analysis on the Impacts of Vaccination and Treatment in the Control of the COVID-19 Pandemic with Optimal Control","authors":"Alemzewde Ayalew, Yezbalem Molla, Tenaw Tilahun, Tadele Tesfa","doi":"10.1155/2023/8570311","DOIUrl":"https://doi.org/10.1155/2023/8570311","url":null,"abstract":"In this study, a nonlinear deterministic mathematical model that evaluates two important therapeutic measures of the COVID-19 pandemic: vaccination of susceptible and treatment for infected people who are in quarantine, is formulated and rigorously analyzed. Some of the fundamental properties of the model system including existence and uniqueness, positivity, and invariant region of solutions are proved under a certain meaningful set. The model exhibits two equilibrium points: disease-free and endemic equilibrium points under certain conditions. The basic reproduction number, \u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 \u0000 , is derived via the next-generation matrix approach, and the dynamical behavior of the model is explored in detail. The analytical analysis reveals that the disease-free equilibrium solution is locally as well as globally asymptotically stable when the associated basic reproduction number is less than unity which indicates that COVID-19 dies out in the population. Also, the endemic equilibrium point is globally asymptotically stable whenever the associated basic reproduction number exceeds a unity which implies that COVID-19 establishes itself in the population. The sensitivity analysis of the basic reproduction number is computed to identify the most dominant parameters for the spreading out as well as control of infection and should be targeted by intervention strategies. Furthermore, we extended the considered model to optimal control problem system by introducing two time-dependent variables that represent the educational campaign to susceptibles and continuous treatment for quarantined individuals. Finally, some numerical results are illustrated to supplement the analytical results of the model using MATLAB ode45.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"68 1","pages":"8570311:1-8570311:15"},"PeriodicalIF":0.0,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79470162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The objective of this work is to investigate the influences of thermal radiation, heat generation, and buoyancy force on the time-dependent boundary layer (BL) flow across a vertical permeable plate. The fluid is unsteady, incompressible, viscous, and electrically insulating. The heat transfer mechanism happens due to free convection. The nondimensional partial differential equations of continuity, momentum, energy, and concentration are discussed using appropriate transformations. The impressions of thermal radiation and buoyancy forces are exposed in the energy and momentum equation, respectively. For numerical model, a set of nonlinear dimensionless partial differential equations can be solved using an explicit finite difference approach. The stability and convergence analyses are also established to complete the formulation of the model. The thermophysical effects of entering physical parameters on the flow, thermal, and material fields are analyzed. The variations in local and average skin friction, material, and heat transfer rates are also discussed for the physical interest. The analysis of the obtained findings is shown graphically, and relevant parameters pointedly prejudice the flow field. Studio Developer FORTRAN 6.2 and Tecplot 10.0 are applied to simulate the schematic model equations and graphical presentation numerically. The intensifying values of the magnetic field are affected decreasingly in the flow field. The temperature profiles decrease within the BL to increase the value of radiation parameters. The present study is on the consequences for petroleum engineering, agriculture engineering, extraction, purification processes, nuclear power plants, gas turbines, etc. To see the rationality of the present research, we compare these results and the results available in the literature with outstanding compatibility.
{"title":"A Numerical Assessment of Time-Dependent Magneto-Convective Thermal-Material Transfer over a Vertical Permeable Plate","authors":"M. J. Uddin, R. Nasrin","doi":"10.1155/2023/9977857","DOIUrl":"https://doi.org/10.1155/2023/9977857","url":null,"abstract":"The objective of this work is to investigate the influences of thermal radiation, heat generation, and buoyancy force on the time-dependent boundary layer (BL) flow across a vertical permeable plate. The fluid is unsteady, incompressible, viscous, and electrically insulating. The heat transfer mechanism happens due to free convection. The nondimensional partial differential equations of continuity, momentum, energy, and concentration are discussed using appropriate transformations. The impressions of thermal radiation and buoyancy forces are exposed in the energy and momentum equation, respectively. For numerical model, a set of nonlinear dimensionless partial differential equations can be solved using an explicit finite difference approach. The stability and convergence analyses are also established to complete the formulation of the model. The thermophysical effects of entering physical parameters on the flow, thermal, and material fields are analyzed. The variations in local and average skin friction, material, and heat transfer rates are also discussed for the physical interest. The analysis of the obtained findings is shown graphically, and relevant parameters pointedly prejudice the flow field. Studio Developer FORTRAN 6.2 and Tecplot 10.0 are applied to simulate the schematic model equations and graphical presentation numerically. The intensifying values of the magnetic field are affected decreasingly in the flow field. The temperature profiles decrease within the BL to increase the value of radiation parameters. The present study is on the consequences for petroleum engineering, agriculture engineering, extraction, purification processes, nuclear power plants, gas turbines, etc. To see the rationality of the present research, we compare these results and the results available in the literature with outstanding compatibility.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"8 1","pages":"9977857:1-9977857:19"},"PeriodicalIF":0.0,"publicationDate":"2023-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88763245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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