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Spatially explicit effective reproduction numbers from incidence and mobility data

Enrico Bertuzzo, Marino Gatto, Lorenzo Mari, Damiano Pasetto, Andrea Rinaldo, Cristiano Trevisin

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, ℛk(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 ℛk(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.

2023

Epidemicity of cholera spread and the fate of infection control measures

Marino Gatto, Joseph Chadi Benoit Lemaitre, Lorenzo Mari, Damiano Pasetto, Andrea Rinaldo, Cristiano Trevisin

The fate of ongoing infectious disease outbreaks is predicted through reproduction numbers, defining the long-term establishment of the infection, and epidemicity indices, tackling the reactivity of the infectious pool to new contagions. Prognostic metrics of unfolding outbreaks are of particular importance when designing adaptive emergency interventions facing real-time assimilation of epidemiological evidence. Our aim here is twofold. First, we propose a novel form of the epidemicity index for the characterization of cholera epidemics in spatial models of disease spread. Second, we examine in hindsight the survey of infections, treatments and containment measures carried out for the now extinct 2010–2019 Haiti cholera outbreak, to suggest that magnitude and timing of non-pharmaceutical and vaccination interventions imply epidemiological responses recapped by the evolution of epidemicity indices. Achieving negative epidemicity greatly accelerates fading of infections and thus proves a worthwhile target of containment measures. We also show that, in our model, effective reproduction numbers and epidemicity indices are explicitly related. Therefore, providing an upper bound to the effective reproduction number (significantly lower than the unit threshold) warrants negative epidemicity and, in turn, a rapidly fading outbreak preventing coalescence of sparse local sub-threshold flare-ups.

2022