两组流行病学模型:稳定性分析及神经网络数值模拟

IF 0.9 Q3 COMPUTER SCIENCE, THEORY & METHODS International Journal of Modeling Simulation and Scientific Computing Pub Date : 2022-07-25 DOI:10.1142/s1793962323500290
M. A. El Yamani, Jaafar El Karkri, S. Lazaar, R. Aboulaich
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引用次数: 0

摘要

这项工作有两个主要目标。首先,我们研究了两组流行病学模型的渐近行为,并利用基于相对矩阵谱半径的动力系统方法确定了其基本再现数的表达式。其次,我们使用一种新的深度学习方法模拟得到的分析结果,该方法将控制模型的常微分方程与神经网络联系起来。考虑了一般的无病平衡点,给出了稳定性和收敛性的充分条件。对仿真中使用的神经网络模型进行了详细的描述。此外,将所提出的深度学习仿真算法与“odeint”提供的仿真进行了比较,“odeint”是一个来自Python数学例程库“SciPy”的函数。
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A two-group epidemiological model: Stability analysis and numerical simulation using neural network
This work has two principal goals. First, we investigate the asymptotic behavior of a two-group epidemiological model and determine the expression of its basic reproduction number using the dynamical systems approach based on the spectral radius of the relative matrix. Second, we simulate the obtained analytical results using a new deep learning method that associates the ordinary differential equations governing the model to neural networks. A general disease-free equilibrium is considered and sufficient conditions of stability and convergence are formulated. A detailed description of the neural network model used in the simulation is provided. Moreover, the proposed deep learning simulation algorithm is compared to the simulation provided by "odeint", a function from "SciPy" which is a Python library of mathematical routines.
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CiteScore
2.50
自引率
16.70%
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