Modeling, Inference, and Prediction in Mobility-Based Compartmental Models for Epidemiology
Ning Jiang, Weiqi Chu, Yao Li
TL;DR
This work tackles the overestimation problem of classical homogeneous epidemiological models by introducing mobility-based heterogeneity into compartmental dynamics. It builds a density-based SIRS framework with mobility-resolved compartments $S(m,t)$, $I(m,t)$, and $R(m,t)$ driven by a population mobility distribution $f(m)$, yielding an infinite-dimensional system whose infection term couples across mobility levels. The authors derive a mobility-aware basic reproduction number $\mathcal{R}_0 = \frac{\beta}{\gamma} \langle m^2 f \rangle$ via the next-generation operator and show that the final pandemic size $R_\infty$ is maximized by a Dirac delta mobility, implying heterogeneity reduces final size for the same $\mathcal{R}_0$. They establish identifiability of the mobility distribution from the infected-time-series data and propose a neural-network-based inverse problem framework trained on Gaussian-mixture mobilities to recover $f(m)$ from real data, including COVID-19 datasets, demonstrating that polarized mobility leads to smaller outbreaks than homogeneous assumptions. Overall, this mobility-based approach provides more accurate forecasts and a principled way to infer population mobility from infection data, with potential extensions to richer compartments and policy-adaptation strategies.
Abstract
Classical compartmental models in epidemiology often assume a homogeneous population for simplicity, which neglects the inherent heterogeneity among individuals. This assumption frequently leads to inaccurate predictions when applied to real-world data. For example, evidence has shown that classical models overestimate the final pandemic size in the H1N1-2009 and COVID-19 outbreaks. To address this issue, we introduce individual mobility as a key factor in disease transmission and control. We characterize disease dynamics using mobility distribution functions for each compartment and propose a mobility-based compartmental model that incorporates population heterogeneity. Our results demonstrate that, for the same basic reproduction number, our mobility-based model predicts a smaller final pandemic size compared to the classical models, effectively addressing the common overestimation problem. Additionally, we infer mobility distributions from the time series of the infected population. We provide sufficient conditions for uniquely identifying the mobility distribution from a dataset and propose a machine-learning-based approach to learn mobility from both synthesized and real-world data.