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.

翻译：我们将流行病学与种群动力学模型用概率分布形式重新表述。这使我们能够构造费舍尔信息，并将其解释为一维可微流形的度量。对于可有效用单一自由度描述的系统，我们证明其时间演化完全由该度量所刻画。通过这一方法，我们发现了看似迥异的模型间存在的普适性特征。这进一步促使我们围绕费舍尔度量的零点（对应于概率分布的极值点）重构动力学过程。具体而言，我们提出了一种简洁的度量形式，可解析求解系统动力学，其能够很好地逼近流行病学与种群动力学中多个经典模型的时间演化，从而构建了一个统一的理论框架。