论文标题
分析力学允许在数学流行动力学建模上进行新颖的远景
Analytical Mechanics Allows Novel Vistas on Mathematical Epidemic Dynamics Modelling
论文作者
论文摘要
该贡献旨在从分析力学的角度阐明数学流行动力学建模。为了设定阶段，它重铸了分析力学设置中数学流行动力学的基本SIR模型。因此，它考虑了基本SIR模型的两个可能的重新分析。一方面，建议重新缩放时间，而另一方面，将其转换为坐标，即\ \自变量。在这两种情况下，汉密尔顿的方程式在适合的汉密尔顿和汉密尔顿的原则方面分别以最小的和扩展的阶段和国家空间坐标的方式考虑在适合的拉格朗日方面。详细介绍了有关汉密尔顿和拉格朗日人的各种选择的相应传统转型。最终，这种贡献扩展了从分析力学观点出现的数学流行动力学建模的众多新型远景。结果，人们认为，当分析力学和数学流行动力学建模之间的类比中，有趣且相关的新研究途径开放。
This contribution aims to shed light on mathematical epidemic dynamics modelling from the viewpoint of analytical mechanics. To set the stage, it recasts the basic SIR model of mathematical epidemic dynamics in an analytical mechanics setting. Thereby, it considers two possible re-parameterizations of the basic SIR model. On the one hand, it is proposed to re-scale time, while on the other hand, to transform the coordinates, i.e.\ the independent variables. In both cases, Hamilton's equations in terms of a suited Hamiltonian as well as Hamilton's principle in terms of a suited Lagrangian are considered in minimal and extended phase and state space coordinates, respectively. The corresponding Legendre transformations relating the various options for the Hamiltonians and Lagrangians are detailed. Ultimately, this contribution expands on a multitude of novel vistas on mathematical epidemic dynamics modelling that emerge from the analytical mechanics viewpoint. As result, it is believed that interesting and relevant new research avenues open up when exploiting in depth the analogies between analytical mechanics and mathematical epidemic dynamics modelling.
