基于扩散方程和流行病学方程的流行病学扩散计算模型

G. Lambrou, K. Hatziagapiou, Petros Toumpaniaris, Penelope Konstantina Ioannidou, D. Koutsouris
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引用次数: 0

摘要

虽然已经收集了大量关于疾病及其传播的知识,但更多的是要学习疾病的数学建模。本工作回顾了流行病学扩散模型的现有知识,创建了一种新形式的流行病学扩散方程,并随后将该方程应用于流行病学现象的调查。在这个范围内,作者使用了以前报道过的数学模型,以及求解复杂函数的随机性质的算法方法。特别是,他们使用了动态规划算法、罗宾斯-门罗和基弗-沃尔福威茨随机优化算法、马尔可夫链和元胞自动机。修正后的扩散方程可能为流行病学现象的研究提供一个有用的工具。需要进行更多的研究,以探索其可能性和用途的程度。
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Computational Modelling in Epidemiological Dispersion Using Diffusion and Epidemiological Equations
Although a considerable amount of knowledge is gathered concerning diseases and their transmission, still more is to learn on their mathematical modelling. The present work reviews the existent knowledge on models of epidemiological dispersion, the creation of a new form of an epidemiological diffusion equation, and the subsequent application of this equation to the investigation of epidemiological phenomena. Towards that scope, the authors have used mathematical models which have been previously reported, as well as algorithmic approaches of stochastic nature for the solution of complex functions. In particular, they have used dynamic programming algorithms, Robbins-Monro and Kiefer-Wolfowitz stochastic optimization algorithms, Markov chains and cellular automata. The modified diffusion equation could potentially provide a useful tool to the investigation of epidemiological phenomena. More research is required in order to explore the extent of its possibilities and uses.
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