Computational and Mathematical Methods最新文献_第6页

The Rate of Convergence of the SOR Method in the Positive Semidefinite Case 正半定情况下SOR方法的收敛速度

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Computational and Mathematical Methods Pub Date : 2022-03-02 DOI: 10.1155/2022/6143444

Achiya Dax

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Effect of General Cross-Immunity Protection and Antibody-Dependent Enhancement in Dengue Dynamics 一般交叉免疫保护和抗体依赖性增强在登革热动力学中的作用

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Computational and Mathematical Methods Pub Date : 2022-02-13 DOI: 10.1155/2022/2074325

Vanessa Steindorf, Sergio Oliva, Jianhong Wu, Maíra Aguiar

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Spatially Extended SHAR Epidemiological Framework of Infectious Disease Transmission 传染病传播的空间扩展share流行病学框架

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Computational and Mathematical Methods Pub Date : 2022-02-13 DOI: 10.1155/2022/3304532

Damián Knopoff, Nicole Cusimano, Nico Stollenwerk, Maíra Aguiar

{"title":"Spatially Extended SHAR Epidemiological Framework of Infectious Disease Transmission","authors":"Damián Knopoff, Nicole Cusimano, Nico Stollenwerk, Maíra Aguiar","doi":"10.1155/2022/3304532","DOIUrl":"10.1155/2022/3304532","url":null,"abstract":"<div>\u0000 <p>Mathematical models play an important role in epidemiology. The inclusion of a spatial component in epidemiological models is especially important to understand and address many relevant ecological and public health questions, e.g., when wanting to differentiate transmission patterns across geographical regions or when considering spatially heterogeneous intervention measures. However, the introduction of spatial effects can have significant consequences on the observed model dynamics and hence must be carefully analyzed and interpreted. Cellular automata epidemiological models typically rely on simplified computational grids but can provide valuable insight into the spatial dynamics of transmission within a population by suitably accounting for the connections between individuals in the considered community. In this paper, we describe a stochastic cellular automata disease model based on an extension of the traditional Susceptible-Infected-Recovered (SIR) compartmentalization of the population, namely, the Susceptible-Hospitalized-Asymptomatic-Recovered (SHAR) formulation, in which infected individuals either present a severe form of the disease, thus requiring hospitalization, or belong to the so-called mild/asymptomatic class. The critical transmission threshold is derived analytically in the nonspatial SHAR formulation, and this generalizes previously obtained theoretical results for the SIR model. We present simulation results discussing the effect of key model parameters and of spatial correlations on model outputs and propose an algorithm for tracking the evolution of infection clusters within the considered population. Focusing on the role of import and criticality on the overall dynamics, we conclude that the current spatial setting increases the critical transmission threshold in comparison to the nonspatial model.</p>\u0000 </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/3304532","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79784711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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A Cell-Centered Semi-Lagrangian Finite Volume Method for Solving Two-Dimensional Coupled Burgers’ Equations 求解二维耦合Burgers方程的半拉格朗日有限体积法

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Computational and Mathematical Methods Pub Date : 2022-02-13 DOI: 10.1155/2022/8192192

Ilham Asmouh, Mofdi El-Amrani, Mohammed Seaid, Naji Yebari

{"title":"A Cell-Centered Semi-Lagrangian Finite Volume Method for Solving Two-Dimensional Coupled Burgers’ Equations","authors":"Ilham Asmouh, Mofdi El-Amrani, Mohammed Seaid, Naji Yebari","doi":"10.1155/2022/8192192","DOIUrl":"10.1155/2022/8192192","url":null,"abstract":"<div>\u0000 <p>A cell-centered finite volume semi-Lagrangian method is presented for the numerical solution of two-dimensional coupled Burgers’ problems on unstructured triangular meshes. The method combines a modified method of characteristics for the time integration and a cell-centered finite volume for the space discretization. The new method belongs to fractional-step algorithms for which the convection and the viscous parts in the coupled Burgers’ problems are treated separately. The crucial step of interpolation in the convection step is performed using two local procedures accounting for the element where the departure point is located. The resulting semidiscretized system is then solved using a third-order explicit Runge-Kutta scheme. In contrast to the Eulerian-based methods, we apply the new method for each time step along the characteristic curves instead of the time direction. The performance of the current method is verified using different examples for coupled Burgers’ problems with known analytical solutions. We also apply the method for simulation of an example of coupled Burgers’ flows in a complex geometry. In these test problems, the new cell-centered finite volume semi-Lagrangian method demonstrates its ability to accurately resolve the two-dimensional coupled Burgers’ problems.</p>\u0000 </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/8192192","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84834098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Study of a Set of Symmetric Temporal Transformations for the Study of the Orbital Motion 研究轨道运动的一组对称时间变换的研究

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Computational and Mathematical Methods Pub Date : 2022-02-13 DOI: 10.1155/2022/9037530

José Antonio López Ortí, Vicente Agost Gómez, Miguel Barreda Rochera

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Deterministic and Stochastic Dynamics of COVID-19: The Case Study of Italy and Spain COVID-19的确定性和随机动力学:以意大利和西班牙为例

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Computational and Mathematical Methods Pub Date : 2022-02-13 DOI: 10.1155/2022/5780719

Akhil Kumar Srivastav, Nico Stollenwerk, Maíra Aguiar

{"title":"Deterministic and Stochastic Dynamics of COVID-19: The Case Study of Italy and Spain","authors":"Akhil Kumar Srivastav, Nico Stollenwerk, Maíra Aguiar","doi":"10.1155/2022/5780719","DOIUrl":"10.1155/2022/5780719","url":null,"abstract":"<div>\u0000 <p>In December 2019, a severe respiratory syndrome (COVID-19) caused by a new coronavirus (SARS-CoV-2) was identified in China and spread rapidly around the globe. COVID-19 was declared a pandemic by the World Health Organization (WHO) in March 2020. With eventually substantial global underestimation, more than 225 million cases were confirmed by the end of August 2021, counting more than 4.5 million deaths. COVID-19 symptoms range from mild (or no symptoms) to severe illness, with disease severity and death occurring according to a hierarchy of risks, with age and preexisting health conditions enhancing the risks of disease severity manifestation. In this paper, a mathematical model for COVID-19 transmission is proposed and analyzed. The model stratifies the studied population into two groups, older and younger. Applied to the COVID-19 outbreaks in Spain and in Italy, we find the disease-free equilibrium and the basic reproduction number for each case study. A sensitivity analysis to identify the key parameters which influence the basic reproduction number, and hence regulate the transmission dynamics of COVID-19, is also performed. Finally, the model is extended to its stochastic counterpart to encapsulate the variation or uncertainty found in the transmissibility of the disease. We observe the variability of the infectious population finding its distribution at a given time, demonstrating that for small populations, stochasticity will play an important role.</p>\u0000 </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/5780719","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81061582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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Improved Shape Parameter Estimation for the Three-Parameter Log-Logistic Distribution 三参数logistic分布的改进形状参数估计

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Computational and Mathematical Methods Pub Date : 2022-02-13 DOI: 10.1155/2022/8400130

Ayana Mateus, Frederico Caeiro

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A Numerical Approach for Singularly Perturbed Nonlinear Delay Differential Equations Using a Trigonometric Spline 奇异摄动非线性时滞微分方程的三角样条数值解法

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Computational and Mathematical Methods Pub Date : 2022-02-13 DOI: 10.1155/2022/8338661

M. Lalu, K. Phaneendra

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A New Probability Model Based on a Coherent System with Applications 一种新的基于相干系统的概率模型及其应用

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Computational and Mathematical Methods Pub Date : 2022-02-13 DOI: 10.1155/2022/8564465

Christophe Chesneau, Hassan S. Bakouch, Bilal A. Para, Mohammad H. Poursaeed

引用次数: 0

Deep Brain Stimulation with a Computational Model for the Cortex-Thalamus-Basal-Ganglia System and Network Dynamics of Neurological Disorders 深部脑刺激与皮层-丘脑-基底神经节系统的计算模型和神经系统疾病的网络动力学

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Computational and Mathematical Methods Pub Date : 2022-02-13 DOI: 10.1155/2022/8998150

Hina Shaheen, Roderick Melnik

{"title":"Deep Brain Stimulation with a Computational Model for the Cortex-Thalamus-Basal-Ganglia System and Network Dynamics of Neurological Disorders","authors":"Hina Shaheen, Roderick Melnik","doi":"10.1155/2022/8998150","DOIUrl":"10.1155/2022/8998150","url":null,"abstract":"<div>\u0000 <p>Deep brain stimulation (DBS) can alleviate the movement disorders like Parkinson’s disease (PD). Indeed, it is known that aberrant beta (13-30 Hz) oscillations and the loss of dopaminergic neurons in the basal ganglia-thalamus (BGTH) and cortex characterize the akinesia symptoms of PD. However, the relevant biophysical mechanism behind this process still remains unclear. Based on the prior striatal inhibitory model, we propose an extended BGTH model incorporating medium spine neurons (MSNs) and fast-spiking interneurons (FSIs) along with the effect of DBS. We are focusing in this paper on an open-loop DBS mode, where the stimulation parameters stay constant independent of variations in the disease state, and modifications of parameters rely mainly on trial and error of medical experts. Additionally, we propose a novel combined model of the cerebellar-basal-ganglia thalamocortical network, MSNs, and FSIs and show new results that indicate that Parkinsonian oscillations in the beta-band frequency range emerge from the dynamics of such a network. Our model predicts that DBS can be used to suppress beta oscillations in globus pallidus pars interna (GPi) neurons. This research will help our better understanding of the changes in the brain activity caused by DBS, providing new insight for studying PD in the future.</p>\u0000 </div>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"2022 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1155/2022/8998150","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82439332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0