An Efficient Computational Numerical Approach For Nonlinear Mathematical Influenza Disease Modelling

2021 ◽  
Author(s):  
Zulqurnain Sabir ◽  
Muhammad Asif Zahoor Raja ◽  
Mohamed R. Ali ◽  
Adnène Arbi ◽  
Muhammad Kristiawan
Keyword(s):  
Numerical Scheme ◽  
Reference Data ◽  
Disease Model ◽  
Numerical Approach ◽  
Disease Modelling ◽  
Mean Square ◽  
Levenberg Marquardt ◽  
Effectiveness And Efficiency ◽  
Comparison Of The Results ◽  
And Training

Abstract In this study, an advanced computational numerical scheme based on the Levenberg-Marquardt backpropagation (LMB) neural network (NN) process, i.e., LMB-NN is presented for solving the nonlinear mathematical influenza disease model. The nonlinear mathematical influenza disease model depends on four categories named susceptible S(t), infected I(t), recovered R(t) and cross-immune individuals proportion C(t). Six different cases of the nonlinear mathematical influenza disease model have been numerically treated using the LMB-NN process and the comparison of the results has been presented by using the reference data-based solutions designed based on the Adams results. The numerically obtained results of the nonlinear mathematical influenza disease model using the verification, testing, and training procedures are calculated using the LMB-NN process to reduce the functions of mean square error (MSE). For the correctness, competence, effectiveness, and efficiency of the LMB-NN process, the proportional and analysis methods are performed using the analysis of correlation, MSE results, error histograms and regression.

scholarly journals Solving an Infectious Disease Model considering Its Anatomical Variables with Stochastic Numerical Procedures

2022 ◽  
Vol 2022 ◽  
pp. 1-12
Author(s):  
Zulqurnain Sabir ◽  
Muhammad Asif Zahoor Raja ◽  
Yolanda Guerrero Sánchez
Keyword(s):  
Infectious Disease ◽  
Disease Model ◽  
Mean Square ◽  
Artificial Neuron ◽  
Infectious Disease Model ◽  
Neuron Networks ◽  
Levenberg Marquardt ◽  
The Mean ◽  
Predator Model ◽  
Infected Prey

The aim of the current work is to perform the numerical investigation of the infectious disease based on the nonlinear fractional order prey-predator model using the Levenberg–Marquardt backpropagation (LMB) based on the artificial neuron networks (ANNs), i.e., LMBNNs. The fractional prey-predator model is classified into three categories, the densities of the susceptible, infected prey, and predator populations. The statistics proportions for solving three different variations of the infectious disease based on the fractional prey-predator model are designated for training 80% and 10% for both validation and testing. The numerical actions are performed using the LMBNNs to solve the infectious disease based on the fractional prey-predator model, and comparison is performed using the database Adams–Bashforth–Moulton approach. The infectious disease based on the fractional prey-predator model is solved using the LMBNNs to reduce the mean square error (M.S.E). In order to validate the exactness, capability, consistency, and competence of the proposed LMBNNs, the numerical procedures using the correlation, M.S.E, regression, and error histograms are drawn.

PARALLEL SOLVER FOR THE SIMULATIONS OF DETONATION WAVES ON UNSTRUCTURED GRIDS

2020 ◽  
Author(s):  
A. I. Lopato ◽  
◽  
A. G. Eremenko ◽  
Keyword(s):  
Chemical Kinetics ◽  
Numerical Scheme ◽  
Unstructured Grids ◽  
Numerical Study ◽  
Numerical Approach ◽  
Detonation Waves ◽  
Detailed Chemical Kinetics ◽  
Parallel Solver ◽  
Further Development ◽  
Detailed Chemical

Recently, we developed a numerical approach for the simulation of detonation waves on fully unstructured grids and applied it to the numerical study of the mechanisms of detonation initiation in multifocusing systems. Current work is devoted to further development of our numerical approach, namely, parallelization of the numerical scheme and introduction of more comprehensive detailed chemical kinetics scheme.

scholarly journals Q-Matrix Refinement Based on Item Fit Statistic RMSEA

2018 ◽  
Vol 43 (7) ◽  
pp. 527-542 ◽  
Author(s):  
Chunhua Kang ◽  
Yakun Yang ◽  
Pingfei Zeng
Keyword(s):  
Search Algorithm ◽  
Delta Method ◽  
Mean Square ◽  
Simulation Studies ◽  
Response Data ◽  
Item Fit ◽  
Dina Model ◽  
Q Matrix ◽  
Diagnosis Model ◽  
Effectiveness And Efficiency

A Q-matrix, which reflects how attributes are measured for each item, is necessary when applying a cognitive diagnosis model to an assessment. In most cases, the Q-matrix is constructed by experts in the field and may be subjective and incorrect. One efficient method to refine the Q-matrix is to employ a suitable statistic that is calculated using response data. However, this approach is limited by its need to estimate all items in the Q-matrix even if only some are incorrect. To address this challenge, this study proposes an item fit statistic root mean square error approximation (RMSEA) for validating a Q-matrix with the deterministic inputs, noisy, “and” (DINA) model. Using a search algorithm, two simulation studies were performed to evaluate the effectiveness and efficiency of the proposed method at recovering Q-matrices. Results showed that using RMSEA can help define attributes in a Q-matrix. A comparison with the existing Delta method and residual sum of squares (RSS) method revealed that the proposed method had higher mean recovery rates and can be used to identify and correct Q-matrix misspecifications. When no error exists in the Q-matrix, the proposed method does not modify the correct Q-matrix.

scholarly journals Solving Mixed Volterra - Fredholm Integral Equation (MVFIE) by Designing Neural Network

2019 ◽  
Vol 16 (1) ◽  
pp. 0116
Author(s):  
Al-Saif Et al.
Keyword(s):  
Neural Network ◽  
Integral Equation ◽  
Analytic Solution ◽  
Fredholm Integral Equations ◽  
Training Algorithm ◽  
Output Unit ◽  
Feed Forward Neural Network ◽  
Levenberg Marquardt ◽  
Hidden Layer ◽  
And Training

       In this paper, we focus on designing feed forward neural network (FFNN) for solving Mixed Volterra – Fredholm Integral Equations (MVFIEs) of second kind in 2–dimensions. in our method, we present a multi – layers model consisting of a hidden layer which has five hidden units (neurons) and one linear output unit. Transfer function (Log – sigmoid) and training algorithm (Levenberg – Marquardt) are used as a sigmoid activation of each unit. A comparison between the results of numerical experiment and the analytic solution of some examples has been carried out in order to justify the efficiency and the accuracy of our method.                                  

scholarly journals Modelling Hourly Global Horizontal Irradiance from Satellite-Derived Datasets and Climate Variables as New Inputs with Artificial Neural Networks

Energies ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 148 ◽  
Author(s):  
Bikhtiyar Ameen ◽  
Heiko Balzter ◽  
Claire Jarvis ◽  
James Wheeler
Keyword(s):  
Test Data ◽  
Sunshine Duration ◽  
Mean Square ◽  
Climate Variables ◽  
Accurate Data ◽  
Training Algorithm ◽  
Clear Sky ◽  
Levenberg Marquardt ◽  
Artificial Neural ◽  
Input Variables

More accurate data of hourly Global Horizontal Irradiance (GHI) are required in the field of solar energy in areas with limited ground measurements. The aim of the research was to obtain more precise and accurate hourly GHI by using new input from Satellite-Derived Datasets (SDDs) with new input combinations of clear sky (Cs) and top-of-atmosphere (TOA) irradiance on the horizontal surface and with observed climate variables, namely Sunshine Duration (SD), Air Temperature (AT), Relative Humidity (RH) and Wind Speed (WS). The variables were placed in ten different sets as models in an artificial neural network with the Levenberg–Marquardt training algorithm to obtain results from training, validation and test data. It was applied at two station types in northeast Iraq. The test data results with observed input variables (correlation coefficient (r) = 0.755, Root Mean Square Error (RMSE) = 33.7% and bias = 0.3%) are improved with new input combinations for all variables (r = 0.983, RMSE = 9.5% and bias = 0.0%) at four automatic stations. Similarly, they improved at five tower stations with no recorded SD (from: r = 0.601, RMSE = 41% and bias = 0.7% to: r = 0.976, RMSE = 11.2% and bias = 0.0%). The estimation of hourly GHI is slightly enhanced by using the new inputs.

scholarly journals Rapid Determination of Aesculin, Aesculetin and Fraxetin inCortex FraxiniExtract Solutions Based on Ultraviolet Spectroscopy

2011 ◽  
Vol 8 (s1) ◽  
pp. S225-S236 ◽  
Author(s):  
Ming Yang ◽  
Jia-Lei Chen ◽  
Xiu-Feng Shi ◽  
Hui-Jue Niu
Keyword(s):  
Root Mean Square Error ◽  
Reference Data ◽  
Rapid Determination ◽  
Ultraviolet Spectroscopy ◽  
Mean Square ◽  
Chemical Parameters ◽  
Ultraviolet Spectra ◽  
Calibration Models ◽  
The Relationship

To evaluate the application of ultraviolet spectroscopy for the rapid determination of aesculin, aesculetin and fraxetin inCortex fraxiniextract solutions, ultraviolet spectra ofCortex fraxiniextract solutions from different batches were collected in the spectral range from 200 nm to 400 nm. The relationship between ultraviolet spectra and chemical parameters displayed some non-linear characteristics. Thus, K-OPLS was proposed to establish the calibration models for the determination ofCortex fraxiniextract solutions between the reference data and ultraviolet spectra. The calibration results were achieved for the determination ofCortex fraxiniextract solutions. The coefficients of determination in calibration (R2) for aesculin, aesculetin and fraxetin were 0.989, 0.957 and 0.939, while in prediction (R2) were 0.982, 0.979 and 0.962, respectively. And the root-mean-square error of prediction (RMSEP) for aesculin, aesculet and fraxetin were 11.99, 3.02 and 1.59 μg/mL. The results demonstrated that ultraviolet spectroscopy could be used for the rapid determination of these three components inCortex fraxiniextract solutions.

scholarly journals Numerical Approach to the Kinematic Analysis of Deployable Structures Forming a Closed Loop

2006 ◽  
Vol 220 (7) ◽  
pp. 1045-1056 ◽  
Author(s):  
W W Gan ◽  
S Pellegrino
Keyword(s):  
Systematic Study ◽  
Numerical Scheme ◽  
Closed Loop ◽  
Numerical Approach ◽  
The Other ◽  
Deployable Structures ◽  
Potential Applications ◽  
Motion Range ◽  
Polygonal Shape ◽  
Spatial Linkages

This article is concerned with spatial linkages forming a closed loop. In one extreme configuration (deployed), these linkages form a frame of polygonal shape, such as a square or a hexagon, and in the other extreme (folded), configuration form a tight bundle. Throughout their motion range, they have mobility one. These linkages have potential applications for next-generation deployable spacecraft structures. The article presents a systematic study of the kinematics of closed-loop structures with these special properties and a numerical scheme for simulating their deployment without making any assumptions about particular symmetry features. The proposed simulation technique is applied to three examples that show different behaviour during deployment.

Collocation Method for the Modeling of Membrane Gas Permeation Systems

2015 ◽  
Vol 16 (3-4) ◽  
pp. 141-149
Author(s):  
Anna Feichtinger ◽  
Aleksander Makaruk ◽  
Ewa Weinmüller ◽  
Anton Friedl ◽  
Michael Harasek
Keyword(s):  
Collocation Method ◽  
Numerical Approximation ◽  
Numerical Approach ◽  
Adaptation Strategy ◽  
Gas Permeation ◽  
Computational Time ◽  
Efficient Computation ◽  
Grid Adaptation ◽  
Crucial Feature ◽  
Comparison Of The Results

AbstractIn this work, we describe a numerical method which enables an efficient computation of membrane gas permeation processes that involve multiple membrane stages and multiple gas components. The utilized numerical approach is a collocation method equipped with a grid adaptation strategy based on a dependable error estimate of the numerical approximation. The comparison of the results provided by the collocation method with those calculated from an experimentally validated finite difference method has demonstrated that the accuracy of both numerical approximations is practically the same. However, the current procedure is characterized by a much better computational efficiency that allows to considerably reduce the computational time. This is a crucial feature when combining computation of membrane permeation processes with optimization algorithms. In such a setting the computation of the permeation process is frequently repeated and naturally, results in long computational times when the efficiency is not adequately improved.

scholarly journals A Fractional-Order Sequential Hybrid System with an Application to a Biological System

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Hasib Khan ◽  
Hashim M. Alshehri ◽  
Zareen A. Khan
Keyword(s):  
Fixed Point ◽  
Fractional Order ◽  
Numerical Scheme ◽  
Real Life ◽  
Numerical Approach ◽  
Existence Results ◽  
Alternative Theorem ◽  
Fixed Point Approach ◽  
Fractional Differential ◽  
Fractional Orders

With the help of Banach’s fixed-point approach and the Leray–Schauder alternative theorem, we produced existence results for a general class of fractional differential equations in this paper. The proposed problem is more comprehensive and applicable to real-life situations. As an example of how our problem might be used, we have created a fractional-order COVID-19 model whose solution is guaranteed by our results. We employed a numerical approach to solve the COVID-19 model, and the results were compared for different fractional orders. Our numerical results for fractional orders follow the same pattern as the classical example of order 1, indicating that our numerical scheme is accurate.

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