Incorporating Spatial Autocorrelation into Optimal Mobility Control Models in Epidemics: A Case Study using Moran’s  I  Statistic

Abstract

Human mobility plays a key role in many epidemics, as evident during the COVID-19 pandemic. As a control measure, mobility restrictions are implemented in and between spatial units, such as states, districts, and local municipalities. The spatial autocorrelation of incidence of disease allows health authorities to decide the mobility restrictions of a spatial unit by observing the incidence of neighboring units. Such a case is tested in this work using a Susceptible-Infected-Recovered (SIR) model for COVID-19 that emphasizes the use of Moran’s $I$ as a measure of spatial autocorrelation. The model is equipped with a parametric design that assimilates the spatial variation of incidence into mobility control. The clustering effect given by positive autocorrelation is observed as a risky case for transmission that calls for severe restrictions. The model is later adapted into an optimal control scenario that addresses the fact that a country should be open to usual economic activities while ensuring lower transmission. Numerical experiments show how Moran’s $I$ classifies transmission risk to achieve optimal mobility control. This approach of incorporating spatial autocorrelation can be used in similar contexts of other dynamical systems.