Harnessing Control Theory, Data Analysis, and a Stochastic Data Assimilation Method to Assess Optimal Mobility Strategies for Epidemics

Overview & Synopsis

Human mobility plays a crucial role in the spatial spread of epidemics within a metapopulation. Consequently, restricting mobility can help limit disease transmission. This raises an important question: how can human movement be optimally regulated within a metapopulation to mitigate potential outbreaks in an endemic context? In this study, we address this question from a mathematical perspective. We propose an SIR epidemic model that incorporates mobility between multiple patches and analyze its dynamics. As our focus is on the spread and control of short-term infectious diseases, demographic processes such as natality and mortality are neglected. In particular, we compute the steady states, derive the basic reproduction number, and establish conditions for epidemic take-o. Using Pontryagin's Maximum Principle (PMP), we analytically determine the optimal mobility rates that can prevent or reduce disease spread. To validate our approach, we apply the framework to data from the late phase of the SARS-CoV-2 pandemic in France. We analyze the eects of governmentimposed control measures, such as curfews, lockdowns, restrictions on public gatherings, and the closure of parks, coee, and restaurants, on mobility patterns and infection dynamics. We tune and validate the model using the Ensemble Kalman Filter (EnKF), estimate the parameters, and compute the optimal mobility matrices. Our results indicate that implementing the derived optimal mobility patterns would have reduced transmission by approximately 84% in France.