A Linear Dynamical Perspective on Epidemiology: Interplay Between Early COVID-19 Outbreak and Human Mobility

TL;DR

This study uses a data-driven Koopman operator framework to model and forecast early COVID-19 spread based on human mobility patterns, revealing a leader-follower relationship and accurately predicting infection numbers.

Contribution

It introduces a novel application of the Koopman framework with control inputs to model epidemic dynamics from data without physical laws, capturing mobility's impact on COVID-19 spread.

Findings

The model accurately forecasts COVID-19 infections for 2-4 week windows.

Identifies a leader-follower relationship between mobility and disease spread.

Demonstrates the effectiveness of the HDMDc algorithm in epidemic modeling.

Abstract

This paper investigates the impact of human activity and mobility (HAM) in the spreading dynamics of an epidemic. Specifically, it explores the interconnections between HAM and its effect on the early spread of the COVID-19 virus. During the early stages of the pandemic, effective reproduction numbers exhibited a high correlation with human mobility patterns, leading to a hypothesis that the HAM system can be studied as a coupled system with disease spread dynamics. This study applies the generalized Koopman framework with control inputs to determine the nonlinear disease spread dynamics and the input-output characteristics as a locally linear controlled dynamical system. The approach solely relies on the snapshots of spatiotemporal data and does not require any knowledge of the system's physical laws. We exploit the Koopman operator framework by utilizing the Hankel Dynamic Mode Decomposition with Control (HDMDc) algorithm to obtain a linear disease spread model incorporating human mobility as a control input. The study demonstrated that the proposed methodology could capture the impact of local mobility on the early dynamics of the ongoing global pandemic. The obtained locally linear model can accurately forecast the number of new infections for various prediction windows ranging from two to four weeks. The study corroborates a leader-follower relationship between mobility and disease spread dynamics. In addition, the effect of delay embedding in the HDMDc algorithm is also investigated and reported. A case study was performed using COVID infection data from Florida, US, and HAM data extracted from Google community mobility data report.