Classical compartmental models in epidemiology often struggle to accurately capture real-world dynamics due to their inability to address the inherent heterogeneity of populations. In this paper, we introduce a novel approach that incorporates heterogeneity through a mobility variable, transforming the traditional ODE system into a system of integro-differential equations that describe the dynamics of population densities across different compartments. Our results show that, for the same basic reproduction number, our mobility-based model predicts a smaller final pandemic size compared to classic compartmental models, whose population densities are represented as Dirac delta functions in our density-based framework. This addresses the overestimation issue common in many classical models. Additionally, we demonstrate that the time series of the infected population is sufficient to uniquely identify the mobility distribution. We reconstruct this distribution using a machine-learning-based framework, providing both theoretical and algorithmic support to effectively constrain the mobility-based model with real-world data.

翻译：经典的流行病学仓室模型由于无法处理人群固有的异质性，往往难以准确捕捉现实世界的动态。本文提出了一种通过引入移动性变量来纳入异质性的新方法，将传统的常微分方程组转化为描述不同仓室间人口密度动态的积分-微分方程组。我们的结果表明，在相同基本再生数条件下，基于移动性的模型预测的最终疫情规模小于经典仓室模型；在本文的密度框架中，经典模型的人口密度可表示为狄拉克δ函数。这一发现解决了经典模型中普遍存在的高估问题。此外，我们证明了感染人群的时间序列足以唯一确定移动性分布。我们采用基于机器学习的框架重建该分布，为利用实际数据有效约束基于移动性的模型提供了理论与算法支持。