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Corruption dynamics: a mathematical model and analysis 腐败动态：数学模型与分析
Frontiers in Applied Mathematics and Statistics Pub Date : 2024-05-13 DOI: 10.3389/fams.2024.1323479
Beza Zeleke Aga, Hika Gemechu Tasisa, T. Keno, Adugna Gadisa Geleta, Dechasa Wegi Dinsa, Abebe Geletu
{"title":"Corruption dynamics: a mathematical model and analysis","authors":"Beza Zeleke Aga, Hika Gemechu Tasisa, T. Keno, Adugna Gadisa Geleta, Dechasa Wegi Dinsa, Abebe Geletu","doi":"10.3389/fams.2024.1323479","DOIUrl":"https://doi.org/10.3389/fams.2024.1323479","url":null,"abstract":"This study proposes and analyzes a deterministic mathematical model to describe the dynamics of corruption transmission. We began by proving that the solution to the model is bounded and positive. The next-generation matrix approach is used to compute the basic reproduction number (R0) in relation to corruption-free equilibrium. The Jacobian and Lyapunov functions are used to show that corruption-free equilibrium is asymptotically stable in both locally and globally when R0<1, and otherwise, an endemic corruption equilibrium develops. Furthermore, the sensitivity of the model's parameters was investigated. The findings demonstrate that religious precepts govern public education. The two sectors most susceptible to corruption control are education and corrections. The study recommends investing more in the provision of public education to citizens by creating awareness among all and including it in the education curriculum and religious leaders to teach their followers seriously about the impact of corruption as well as the use of jail as punishment. The numerical simulation results agreed with the analytical results.","PeriodicalId":507585,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140985938","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}
引用次数: 0
Beta transformation of the Exponential-Gaussian distribution with its properties and applications 指数-高斯分布的贝塔变换及其特性和应用
Frontiers in Applied Mathematics and Statistics Pub Date : 2024-05-10 DOI: 10.3389/fams.2024.1399837
Kumlachew Wubale Tesfaw, A. Goshu
{"title":"Beta transformation of the Exponential-Gaussian distribution with its properties and applications","authors":"Kumlachew Wubale Tesfaw, A. Goshu","doi":"10.3389/fams.2024.1399837","DOIUrl":"https://doi.org/10.3389/fams.2024.1399837","url":null,"abstract":"This study introduces a five-parameter continuous probability model named the Beta-Exponential-Gaussian distribution by extending the three-parameter Exponential-Gaussian distribution with the beta transformation method. The basic properties of the new distribution, including reliability measure, hazard function, survival function, moment, skewness, kurtosis, order statistics, and asymptotic behavior, are established. Using the acceptance-rejection algorithm, simulation studies are conducted. The new model is fitted to the simulated and real data sets, and its performance is reported. The Beta-Exponential-Gaussian distribution is found to be more flexible and has better performance in many aspects. It is suggested that the new distribution would be used in modeling data having skewness and bimodal distribution.","PeriodicalId":507585,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140992676","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}
引用次数: 0
Empirical examination of the Black–Scholes model: evidence from the United States stock market 布莱克-斯科尔斯模型的实证研究：来自美国股市的证据
Frontiers in Applied Mathematics and Statistics Pub Date : 2024-05-10 DOI: 10.3389/fams.2024.1216386
Monsurat Foluke Salami
{"title":"Empirical examination of the Black–Scholes model: evidence from the United States stock market","authors":"Monsurat Foluke Salami","doi":"10.3389/fams.2024.1216386","DOIUrl":"https://doi.org/10.3389/fams.2024.1216386","url":null,"abstract":"Option pricing is crucial in enabling investors to hedge against risks. The Black–Scholes option pricing model is widely used for this purpose. This paper investigates whether the Black–Scholes model is a good indicator of option pricing in the United States stock market. We examine the relevance of the Black–Scholes model to certain stocks using paired sample t-test and Corrado and Miller’s approximation for the implied volatility. Empirical tests are applied to determine the significance of the relationship between the actual market values and the Black–Scholes model values. Paired sample t-tests are applied to 582 call options and 579 put options. The empirical test results show that there is no significant difference between the actual market premium value and the Black–Scholes model premium value for seven out of nine stocks considered for call options, and four out of nine stocks considered for put options. Thus, we conclude that the Black–Scholes option pricing model can be used to price call options but is not suitable for pricing put options in the United States stock market.","PeriodicalId":507585,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140991589","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}
引用次数: 0
Mathematical modeling of two strains tuberculosis and COVID-19 vaccination model: a co-infection study with cost-effectiveness analysis 两株结核菌和 COVID-19 疫苗接种模型的数学建模：联合感染研究与成本效益分析
Frontiers in Applied Mathematics and Statistics Pub Date : 2024-05-09 DOI: 10.3389/fams.2024.1373565
Raymond Fosu Appiah, Zhen Jin, Junyuan Yang, Joshua Kiddy K. Asamoah, Yuqi Wen
{"title":"Mathematical modeling of two strains tuberculosis and COVID-19 vaccination model: a co-infection study with cost-effectiveness analysis","authors":"Raymond Fosu Appiah, Zhen Jin, Junyuan Yang, Joshua Kiddy K. Asamoah, Yuqi Wen","doi":"10.3389/fams.2024.1373565","DOIUrl":"https://doi.org/10.3389/fams.2024.1373565","url":null,"abstract":"Tuberculosis and COVID-19 co-infection is currently the major issue of public health in many nations, including Ghana. Therefore, to explore the effects of the two Tuberculosis strains on COVID-19, we suggest a Tuberculosis and COVID-19 co-infection model. The study also provides the most economical and effective control methods to reduce the co-infection of tuberculosis and COVID-19. Based on the behavioral patterns of the two Tuberculosis strains and COVID-19 reproduction numbers, the stability of the co-infection model is examined. We explore the sensitivity of the parameters to examine the effect of the drug-resistant and drug-sensitive strain of Tuberculosis on the co-infection of COVID-19. We determine the most cost-effective and optimal treatment strategies that aim to maximize outcomes while minimizing tuberculosis and/or COVID-19 incidences, cost-effectiveness, and optimization approaches. The outcomes of this work contribute to a better understanding of Tuberculosis and COVID-19 epidemiology and provide insights into implementing interventions needed to minimize Tuberculosis and COVID-19 burden in similar settings worldwide.","PeriodicalId":507585,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140995850","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}
引用次数: 0
Understanding COVID-19 propagation: a comprehensive mathematical model with Caputo fractional derivatives for Thailand 了解 COVID-19 的传播：采用卡普托分数导数的泰国综合数学模型
Frontiers in Applied Mathematics and Statistics Pub Date : 2024-05-09 DOI: 10.3389/fams.2024.1374721
Shamil E, Sayooj Aby Jose, H. S. Panigoro, A. Jirawattanapanit, B. I. Omede, Z. Yaagoub
{"title":"Understanding COVID-19 propagation: a comprehensive mathematical model with Caputo fractional derivatives for Thailand","authors":"Shamil E, Sayooj Aby Jose, H. S. Panigoro, A. Jirawattanapanit, B. I. Omede, Z. Yaagoub","doi":"10.3389/fams.2024.1374721","DOIUrl":"https://doi.org/10.3389/fams.2024.1374721","url":null,"abstract":"This research introduces a sophisticated mathematical model for understanding the transmission dynamics of COVID-19, incorporating both integer and fractional derivatives. The model undergoes a rigorous analysis, examining equilibrium points, the reproduction number, and feasibility. The application of fixed point theory establishes the existence of a unique solution, demonstrating stability in the model. To derive approximate solutions, the generalized Adams-Bashforth-Moulton method is employed, further enhancing the study's analytical depth. Through a numerical simulation based on Thailand's data, the research delves into the intricacies of COVID-19 transmission, encompassing thorough data analysis and parameter estimation. The study advocates for a holistic approach, recommending a combined strategy of precautionary measures and home remedies, showcasing their substantial impact on pandemic mitigation. This comprehensive investigation significantly contributes to the broader understanding and effective management of the COVID-19 crisis, providing valuable insights for shaping public health strategies and guiding individual actions.","PeriodicalId":507585,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140994606","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}
引用次数: 0
Qualitative analysis of solutions for a degenerate partial differential equations model of epidemic spread dynamics 流行病传播动力学退化偏微分方程模型解的定性分析
Frontiers in Applied Mathematics and Statistics Pub Date : 2024-05-02 DOI: 10.3389/fams.2024.1383106
Roman Taranets, Nataliya Vasylyeva, Belgacem Al-Azem
{"title":"Qualitative analysis of solutions for a degenerate partial differential equations model of epidemic spread dynamics","authors":"Roman Taranets, Nataliya Vasylyeva, Belgacem Al-Azem","doi":"10.3389/fams.2024.1383106","DOIUrl":"https://doi.org/10.3389/fams.2024.1383106","url":null,"abstract":"Compartmental models are widely used in mathematical epidemiology to describe the dynamics of infectious diseases or in mathematical models of population genetics. In this study, we study a time-dependent Susceptible-Infectious-Susceptible (SIS) Partial Differential Equation (PDE) model that is based on a diffusion-drift approximation of a probability density from a well-known discrete-time Markov chain model. This SIS-PDE model is conservative due to the degeneracy of the diffusion term at the origin. The main results of this article are the qualitative behavior of weak solutions, the dependence of the local asymptotic property of these solutions on initial data, and the existence of Dirac delta function type solutions. Moreover, we study the long-term behavior of solutions and confirm our analysis with numerical computations.","PeriodicalId":507585,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141022912","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}
引用次数: 0
Covariate adjusted nonparametric methods under propensity analysis 倾向分析下的共变量调整非参数方法
Frontiers in Applied Mathematics and Statistics Pub Date : 2024-03-27 DOI: 10.3389/fams.2024.1357816
Jiabu Ye, Dejian Lai
{"title":"Covariate adjusted nonparametric methods under propensity analysis","authors":"Jiabu Ye, Dejian Lai","doi":"10.3389/fams.2024.1357816","DOIUrl":"https://doi.org/10.3389/fams.2024.1357816","url":null,"abstract":"Propensity score is one of the most commonly used score functions in adjusting for covariates effect in statistical inference. It is important to understand the impact with propensity score in case some of the prespecified covariates are severely imbalanced. In this article, we performed simulation evaluation the empirical type 1 error and empirical power under scenario of imbalanced covariates in several nonparametric two sample tests with propensity score or with other covariate adjustments. Our results suggest common propensity score approaches might have type 1 error inflation at scenarios with severe imbalanced covariates or model is mis-specified.","PeriodicalId":507585,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140373751","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}
引用次数: 0
Optimal control problem for mathematical modeling of Zika virus transmission using fractional order derivatives 利用分数阶导数建立寨卡病毒传播数学模型的优化控制问题
Frontiers in Applied Mathematics and Statistics Pub Date : 2024-03-22 DOI: 10.3389/fams.2024.1376507
A. Kouidere, Amine El Bhih, Issam Minifi, O. Balatif, Khalid Adnaoui
{"title":"Optimal control problem for mathematical modeling of Zika virus transmission using fractional order derivatives","authors":"A. Kouidere, Amine El Bhih, Issam Minifi, O. Balatif, Khalid Adnaoui","doi":"10.3389/fams.2024.1376507","DOIUrl":"https://doi.org/10.3389/fams.2024.1376507","url":null,"abstract":"This study delves into the dynamics of Zika virus transmission by employing a mathematical model to explain virus spread with fractional order derivatives. The population is divided into two groups: the human group and the ticks group to accurately explain the transmission routes of the virus. The objective of this research is to protect susceptible individuals from infection and curb the spread of this endemic disease. To achieve this, we have included two control measures: the first is a sensibilization program, and the second is treatment. We investigate the use of optimal control strategies and fractional derivative techniques under the Caputo method to reduce the number of exposed and infected individuals. By employing the Pontryagin maximum principle to analyze and characterize the optimal controls, the proposed method is further validated through numerical simulations. The outcome of this study highlights the importance of containing the rate of dynamic dissemination in preventing the Zika epidemic.","PeriodicalId":507585,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140211835","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}
引用次数: 0
Removability conditions for anisotropic parabolic equations in a computational validation 计算验证中各向异性抛物方程的可移性条件
Frontiers in Applied Mathematics and Statistics Pub Date : 2024-03-20 DOI: 10.3389/fams.2024.1388810
Dirk Langemann, Mariia Savchenko
{"title":"Removability conditions for anisotropic parabolic equations in a computational validation","authors":"Dirk Langemann, Mariia Savchenko","doi":"10.3389/fams.2024.1388810","DOIUrl":"https://doi.org/10.3389/fams.2024.1388810","url":null,"abstract":"The article investigates removability conditions for singularities of anisotropic parabolic equations and in particular for the anisotropic porous medium equation and it aims in the numerical validation of the analytical results. The preconditions on the strength of the anisotropy are analyzed, and the analytical estimates for the growth behavior of the solutions near the singularities are compared with the observed growth in numerical simulations. Despite classical estimates used in the proof, we find that the analytical estimates are surprisingly close to the numerically observed solution behavior.","PeriodicalId":507585,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140225895","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}
引用次数: 0
Bias reduction of maximum likelihood estimation in exponentiated Teissier distribution 指数化泰西尔分布中最大似然估计的偏差减小
Frontiers in Applied Mathematics and Statistics Pub Date : 2024-03-20 DOI: 10.3389/fams.2024.1351651
Ahmed Abdulhadi Ahmed, Z. Algamal, Olayan Albalawi
{"title":"Bias reduction of maximum likelihood estimation in exponentiated Teissier distribution","authors":"Ahmed Abdulhadi Ahmed, Z. Algamal, Olayan Albalawi","doi":"10.3389/fams.2024.1351651","DOIUrl":"https://doi.org/10.3389/fams.2024.1351651","url":null,"abstract":"The exponentiated Teissier distribution (ETD) offers an alternative for modeling survival data, taking into account flexibility in modeling data with increasing and decreasing hazard rate functions. The most popular method for parameter estimation of the ETD distribution is the maximum likelihood estimation (MLE). The MLE, on the other hand, is notoriously biased for its small sample sizes. We are therefore driven to generate virtually unbiased estimators for ETD parameters. More specifically, we focus on two methods of bias correction, bootstrapping and analytical approaches, to reduce MLE biases to the second order of bias. The performances of these approaches are compared through Monte Carlo simulations and two real-data applications.","PeriodicalId":507585,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140225076","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}
引用次数: 0
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