Spatially explicit effective reproduction numbers from incidence and mobility data

Current methods for near real-time estimation of effective reproduction numbers from surveillance data overlook mobility fluxes of infectors and susceptible individuals within a spatially connected network (the metapopulation). Exchanges of infections among different communities may thus be misrepresented unless explicitly measured and accounted for in the renewal equations. Here, we first derive the equations that include spatially explicit effective reproduction numbers, 9Zk(t), in an arbitrary community k. These equations embed a suitable connection matrix blending mobility among connected communities and mobility-related containment measures. Then, we propose a tool to estimate, in a Bayesian framework involving particle filtering, the values of 9Zk(t) maximizing a suitable likelihood function reproducing observed patterns of infections in space and time. We validate our tools against synthetic data and apply them to real COVID-19 epidemiological records in a severely affected and carefully monitored Italian region. Differences arising between connected and disconnected reproduction numbers (the latter being calculated with existing methods, to which our formulation reduces by setting mobility to zero) suggest that current standards may be improved in their estimation of disease transmission over time.

Automated summary

Current methods for estimating effective reproduction numbers overlook mobility fluxes in a spatially connected network. This study proposes equations that include spatially explicit effective reproduction numbers, 9Zk(t), for different communities and a tool to estimate these values using a Bayesian framework. The results suggest that current standards may underestimate disease transmission over time based on differences between connected and disconnected reproduction numbers.