A linear dynamical perspective on epidemiology: interplay between early COVID-19 outbreak and human mobility

Nonlinear Dyn https://doi.org/10.1007/s11071-022-07469-5 ORIGINAL PAPER A linear dynamical perspective on epidemiology: interplay between early COVID-19 outbreak and human mobility Shakib Mustavee · Shaurya Agarwal · Chinwendu Enyioha · Suddhasattwa Das Received: 24 August 2021 / Accepted: 19 April 2022 © The Author(s), under exclusive licence to Springer Nature B.V. 2022 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 underlying physical laws. We exploit the Koopman operator framework by utilizing the Hankel dynamic mode decomposition with Control S. Mustavee (B) · S. Agarwal Department of Civil Engineering, University of Central Florida, Orlando, FL 32816, USA e-mail: S. Agarwal e-mail: C. Enyioha Department of Electrical and Computer Engineering, University of Central Florida, Orlando, FL 32816, USA e-mail: S. Das Department of Mathematical Sciences, George Mason, University, Fairfax, VA 22030, USA e-mail: (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. Keywords Koopman operator · HDMD · COVID-19 · Human activity and mobility 1 Introduction Given how increasingly connected the world is, epidemics are becoming a commonplace. As we know and have come to see through the ongoing COVID19 pandemic, the significant loss of lives, as well as the short and long-term economic impact, can be very devastating. Besides the loss of lives, the pandemic has also crippled global transportation, food supply, and challenged healthcare systems in ways not seen before. Understanding and forecasting the spread dynamics 123 S. Mustavee et al. is a challenging task, in part because these are high dimensional, nonlinear, and time-varying systems. In addition, the spreading process exhibits a multi-scale spatiotemporal phenomenon [3,11,46]. It depends on many exogenous variables, including human activity and mobility (HAM) and mitigation measures such as vaccination and face coverings adopted by people. HAM is considered a critical factor in the disease spread, given the fact that the effective reproduction number of the pandemic is highly correlated to mobility. During the onset of the ongoing global pandemic, mitigation strategies revolved around imposing various restriction measures on human activity and mobility. Since the first ‘stay-at-home’ order was issued in the USA on March 15, 2020, in Puerto Rico, similar executive orders issued by state and municipal authorities notably curbed travel demand and thus potentially limiting the community spread of COVID-19. Similarly, governmental agencies worldwide have imposed lockdown and introduced various social isolation strategies for controlling the spread of coronavirus. The underlying rationale for these restriction strategies, such as lockdown and social isolation, is to reduce the scope of direct interpersonal contacts, which on the other hand, adversely impact human activity and mobility, in turn, slows down the disease transmission rate. Thus, dynamics of COVID-19 spread and the dynamics of HAM are intertwined via an intricate relationship. Despite the close connections between the spread of a pandemic and mobility, obtaining a quantifiable relationship between them is challenging because the spread dynamics of a pandemic such as COVID-19 depend on various other factors such as social distancing mask-wearing, mutation of the virus, etc. Moreover, mobility is a multi-modal service, which means each mode of mobility has a different mechanism to impact the disease spread dynamics. Thus, Linka et al. [38] characterized mobility as a ‘global barometer’ of COVID-19. Although the literature has, for many decades, proposed ways of modeling epidemic processes in human populations, several factors that affect the rate of spread or control are not often accounted for. For example, human mobility and activity levels in an outbreak can affect how fast the outbreak is contained or how quickly it spreads. While this knowledge, in part, informs the preliminary soft measures typically taken by health policymakers such as social distanc- 123 ing and lockdown, which prevents mobility or travel of individuals between infected and uninfected areas, the degree to which such external factors affect the pace of spread are not often wholly known. A significant research gap that arises here is establishing the interplay between the pandemic dynamics and the HAM changes due to adopted countermeasures (lockdown, social distancing, etc.). This gap in knowledge makes the existing control strategies deviate from arguably optimal approaches based on the actual nonlinear dynamics. For a highly infectious disease like COVID-19, a paradigm shift in characterizing the spreading dynamics is necessary. To contain a resurgence of the outbreak using scarce or limited resources (such as vaccines and ventilators), a reliable approach of integrating HAM into the spread models aided by novel data-driven tools within a rigorous mathematical framework is necessary. The output of the proposed tightly integrated, the equationfree approach can provide more robust analysis and serve as a helpful tool for policymakers. In this paper, we study the interconnections between the simultaneous evolution of two systems—HAM and disease spread—by treating them as a coupled dynamical system (see Fig. 1). This research builds a system discovery framework through the Koopman operator framework exploiting Hankel dynamic mode decomposition with control (HDMDc) algorithm for understanding the dynamics of the COVID-19 disease and its interplay with HAM. (...truncated)