标题： 信息论：流行病学与种群动力学的统一 显示英文标题

标题： Information Theory Unification of Epidemiological and Population Dynamics

摘要： 我们以概率分布的形式重新表述了流行病学和种群动力学中的模型。 这使我们能够构造费雪信息量，并将其解释为一维可微流形的度量。 对于可以通过单一自由度有效描述的系统，我们证明其时间演化完全由该度量捕获。 通过这种方式，我们在看似非常不同的模型之间发现了普遍特征。 这进一步激发了围绕费雪度量零点（对应于概率分布的极值）重新组织动力学的想法。 具体来说，我们提出了一种度量的简单形式，对于这种形式，我们可以解析地求解系统的动力学，该系统很好地近似了流行病学和种群动力学中各种已有模型的时间演化，从而提供了一个统一的框架。 显示英文摘要

摘要： We reformulate models in epidemiology and population dynamics in terms of probability distributions. This allows us to construct the Fisher information, which we interpret as the metric of a one-dimensional differentiable manifold. For systems that can be effectively described by a single degree of freedom, we show that their time evolution is fully captured by this metric. In this way, we discover universal features across seemingly very different models. This further motivates a reorganisation of the dynamics around zeroes of the Fisher metric, corresponding to extrema of the probability distribution. Concretely, we propose a simple form of the metric for which we can analytically solve the dynamics of the system that well approximates the time evolution of various established models in epidemiology and population dynamics, thus providing a unifying framework.