A model based on mobility data explains localization-delocalization properties in the spread of diseases among communities

We investigate the modes of propagation of an epidemic across a network of communities. Specifically, we consider a spatial variant of the famous SIR model. We first show that the infectivity matrix, characterizing the spread of the infection, can be related to the matrix of fluxes between communities, which we obtained from cell phone mobility data recorded in the USA between March 2020 and February 2021. We applied this model to the 2020 pandemic of SARS-CoV-2, and compared its predictions to empirical data. By fitting just one global parameter representing the frequency of interaction between individuals, we found that the number of susceptible and infected individuals predicted by the model agreed with the empirical reports locally, in each community, thus validating our model. The effect of "shelter-in-place" policies instated throughout the USA at the onset of the pandemic is clearly seen in our results. We then consider the effect an alternative policy would have had, namely restricting long-range travels. We find that this policy is successful in decreasing the epidemic size, but it requires a substantial restriction on the distance traveled. Due to the mode of propagation to nearest-neighbors, this policy leads to infection waves. On a simplified two-dimensional rectangular lattice, we show that there is a regime in which an infection wave exists. We give the differential equation satisfied by the wave profile, and show it is in agreement with numerical simulations. We hope this type of approach, integrating real-time measurements into epidemiological models, will lead to accurate short-term predictions about the spread of infectious agents.