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一种利用启发式计算神经网络的冠状病毒传播数学模型。

A mathematical model of coronavirus transmission by using the heuristic computing neural networks.

作者信息

Sabir Zulqurnain, Asmara Adi, Dehraj Sanaullah, Raja Muhammad Asif Zahoor, Altamirano Gilder Cieza, Salahshour Soheil, Sadat R, Ali Mohamed R

机构信息

Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan.

Faculty of Teacher Training and Education, Mathematics Study Program, Universitas Muhammadiyah Bengkulu, Bengkulu, Indonesia.

出版信息

Eng Anal Bound Elem. 2023 Jan;146:473-482. doi: 10.1016/j.enganabound.2022.10.033. Epub 2022 Oct 31.

Abstract

In this study, the nonlinear mathematical model of COVID-19 is investigated by stochastic solver using the scaled conjugate gradient neural networks (SCGNNs). The nonlinear mathematical model of COVID-19 is represented by coupled system of ordinary differential equations and is studied for three different cases of initial conditions with suitable parametric values. This model is studied subject to seven class of human population () and individuals are categorized as: susceptible (), exposed (), quarantined (), asymptotically diseased (), symptomatic diseased () and finally the persons removed from COVID-19 and are denoted by (). The stochastic numerical computing SCGNNs approach will be used to examine the numerical performance of nonlinear mathematical model of COVID-19. The stochastic SCGNNs approach is based on three factors by using procedure of verification, sample statistics, testing and training. For this purpose, large portion of data is considered, i.e., 70%, 16%, 14% for training, testing and validation, respectively. The efficiency, reliability and authenticity of stochastic numerical SCGNNs approach are analysed graphically in terms of error histograms, mean square error, correlation, regression and finally further endorsed by graphical illustrations for absolute errors in the range of 10 to 10 for each scenario of the system model.

摘要

在本研究中,利用缩放共轭梯度神经网络(SCGNNs)通过随机求解器研究了COVID-19的非线性数学模型。COVID-19的非线性数学模型由常微分方程的耦合系统表示,并针对具有合适参数值的三种不同初始条件情况进行了研究。该模型针对七类人群()进行了研究,个体被分类为:易感者()、暴露者()、被隔离者()、无症状感染者()、有症状感染者(),最后是从COVID-19中康复的人,用()表示。将使用随机数值计算SCGNNs方法来检验COVID-19非线性数学模型的数值性能。随机SCGNNs方法基于验证、样本统计、测试和训练过程的三个因素。为此,考虑了大部分数据,即分别将70%、16%、14%的数据用于训练、测试和验证。通过误差直方图、均方误差、相关性、回归等图形方式分析了随机数值SCGNNs方法的效率、可靠性和真实性,最后通过系统模型每种情况在10到10范围内绝对误差的图形说明进一步验证。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a639/9618448/26aa04e3eedf/gr1_lrg.jpg

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