Spatial spread of COVID-19 during the early pandemic phase in Italy – BMC Infectious Diseases – BMC Infectious Diseases

Study population and data

The first autochthonous case of COVID-19 in Italy was microbiologically diagnosed in the Lombardy Region on February 20, 2020. At the time, intensive testing, isolation of confirmed cases, and quarantine of case contacts were in place in the entire country [19]. Following the rapid increase of SARS-CoV-2 laboratory-confirmed infections, local and national health authorities imposed increasingly strict physical distancing measures, with a quarantine imposed on all individuals residing in 10 municipalities in the Lombardy Region and one in the Veneto Region on February 23, 2020 [2]. A regional lockdown in Lombardy and a national lockdown were imposed respectively on March 8 and March 10, 2020 [20]. Applied measures included the suspension of teaching activities and restrictions on individuals movements across different regions and culminated in the closure of all non-essential retail and shops and a stay at home order applied throughout the entire Italian territory.

Since January 2020, data on PCR-confirmed SARS-CoV-2 infections have been collected in the 19 Italian Regions and the two Autonomous Provinces and reported to National Integrated Surveillance System [19]. A central database of all infections confirmed in Italy was formally established the February 27,2020 and managed by the Italian National Institute of Health. For any confirmed infection, information was collected on the date of diagnosis, municipality of residence, and clinical severity; the date of symptom onset was also recorded for symptomatic cases. The initial line list of laboratory-confirmed cases was retrospectively consolidated, through information gathered with standardized interviews to ascertained infections and PCR testing of their close contacts.

Our analysis is based on the consolidated dataset of all ascertained cases with symptom onset between January 26 and March 7, 2020, corresponding to the 6 epidemiological weeks preceding the first regional lockdown imposed in Lombardy on March 8, 2020. We focus our analysis on this period to reduce the potential biases led by the introduction of strict restrictions to the population. Data used to perform the presented analysis were extracted in February 2021.

By adapting a method previously developed to estimate sources and sinks of malaria parasites in Madagascar [21], we investigate the likely source locations of infection of each symptomatic case retrospectively identified by public health authorities in Italy with symptom onset in the 6weeks between January 26 and March 7. For each case residing in municipality i with symptom onset on day t, we describe the risk that the case was infected T days previously because of contacts with people residing in the municipality j as:

$${{text{L}}}_{{text{i}},{text{j}}}left(t,Tright)={C}_{i,j}mathcal{G}left(Tright)frac{{Y}_{j}left(t-Tright)}{{N}_{j}}$$

where ({C}_{i,j}) represents the number of individuals daily traveling from (i) to (j), (mathcal{G}left(Tright)) is the probability distribution of the SARS-CoV-2 generation time (assumed to be equal to the distribution of the serial interval estimated in [2]), ({Y}_{j}left(t-Tright)) is the number of infected individuals residing in j who developed symptoms at time (t-T), and ({N}_{j}) is the total number of individuals residing in j.

The amount of travels across the different municipalities of Italy (({C}_{i,j})) is modeled by means of a radiation model [22], which is based on data on the size of the population residing in each municipality, the distance between their centroids, and the proportion of daily commuters recorded by Italian National Institute of Statistics in 2019 (Figure S1) [23].

We estimate the probability that a case residing in municipality i with symptom onset on dayt, was infected by a case residing in municipality j as:

$${{text{p}}}_{{text{i}},{text{j}}}left(tright)=frac{{sum }_{T=1}^{infty }{L}_{i,j}left(t,Tright)}{{sum }_{j=1}^{M}{sum }_{T=1}^{infty }{L}_{i,j}left(t,Tright)}$$

where M is the total number of municipalities in Italy in 2020 (namely, 7926).

Similarly, the probability that a case residing in municipality i and developing symptoms during the period (uppi) was infected by a case from municipality j is computed as:

$${{text{p}}}_{{text{i}},{text{j}}}left(uppi right)=frac{{sum }_{tinuppi }{p}_{i,j}left(tright){{text{Y}}}_{{text{i}}}left({text{t}}right)}{{sum }_{tinuppi }{{text{Y}}}_{{text{i}}}left({text{t}}right)}.$$

Finally, we estimate the probability that individuals developing symptoms during the period (uppi) were infected within a distance D from their residence as:

$${p}_{D}left(uppi right)=frac{{sum }_{i}{sum }_{j:{d}_{i,j}

where possible sources j run over all municipalities with a distance from i (namely, ({d}_{i,j})) lower than D.

The contribution of each municipality j in the number of infection episodes occurring at time (t) in all the other municipalities of Italy is quantified as ({sum }_{ine j}{p}_{i,j}left(tright){Y}_{i}left(tright)/{sum }_{{text{j}}=1}^{{text{M}}}{sum }_{ine j}{p}_{i,j}left(tright){Y}_{i}left(tright)).

We estimate the number of epidemic foci occurred in Italy up to March 7, 2020. To this aim, we identify for each week (w) those municipalities characterized by a non-negligible number of ascertained symptomatic cases (({sum }_{tin w}{{text{Y}}}_{{text{i}}}left({text{t}}right)>10)) and incidence (({sum }_{tin w}{{text{Y}}}_{{text{i}}}left({text{t}}right)/{{text{N}}}_{{text{i}}}>0.001)), and by the majority of transmission episodes estimated as occurring between individuals residing in the municipality (({p}_{i,i}left(wright)>0.5)).

In the probabilistic approach, we assume that the mobility fluxes among municipalities can be modeled through a radiation model. Although the radiation model has been effectively employed to describe the spatial spread of infectious diseases in high-income countries [22, 24], following the approach already used in Gatto et al. [13], we show that the flows of individuals obtained through the radiation model are in good agreement with mobility data across the 12 provinces of the Lombardy region, based on 2016 census data adjusted with the population projections for 2020 [25] (see Figures S2 and S3). Furthermore, we use a dynamic metapopulation transmission model based on a susceptible-infectious-recovered (SIR) schema to test if the radiation model is reasonably able to capture the observed spatial spread of COVID-19 in Italy and the overall temporal increase of COVID-19 patients across regions from February 1 up to March 7, 2020. To compare model simulations with data, we assume that 3% of all infections were ascertained by public health authorities, either in real time or retrospectively through contact tracing operations and epidemiological investigations [26]. In the dynamic model, infected individuals residing in the municipality j are assumed to exert a time dependent force of infection ({lambda }_{i,j}left(tright)) on individuals residing in municipality (i) defined as ({lambda }_{i,j}left(tright)=beta {C}_{i,j}{I}_{j}left(tright)/{{text{N}}}_{j}), where (beta) is the SARS-CoV-2 transmission rate, ({C}_{i,j}) is the amount of individuals daily traveling from (i) to (j) as obtained by using the radiation model, ({I}_{j}(t)) and ({N}_{j}) are, respectively, the overall number of infectious individuals and the population size in municipality (j). Based on the simulation results, we compute the probability that an individual residing in municipality i and infected at day t was infected by a case from municipality j as ({{text{p}}}_{{text{i}},{text{j}}}left(tright)={uplambda }_{i,j}left(tright)/{sum }_{j=1}^{M}{lambda }_{i,j}left(tright)), with M representing the overall number of municipalities of Italy in 2020; ({{text{p}}}_{{text{i}},{text{j}}}left(uppi right)) is computed as in the probabilistic approach, but using the overall number of infections estimated by the dynamic model instead of the symptomatic cases ascertained in the data. Given the large uncertainty surrounding the ability of the public health system in identifying (either in real time or retrospectively) cases that occurred in the early pandemic phase, we repeat the analysis and estimate the risk of SARS-CoV-2 transmission at different distances by assuming also a 10% ascertainment ratio.

The SIR model is parametrized to reproduce at the national level an epidemic curve associated with an exponential growth rate (r) corresponding to a basic reproduction number ({R}_{0}=2.8), representing the transmissibility potential of SARS-CoV-2, estimated for the Lombardy Region between February 12 and March 9, 2020 [2, 20]. The average duration of the infectivity period is assumed to be equal to the mean serial interval (G) [2]. The ({R}_{0}) associated with the simulated epidemic curve is computed by considering the growth rate (r) associated with the number of new cases simulated by the model at the national level and using the standard equation ({R}_{0}=1+rG). The model is initialized on February 1 (at ({t}_{0}=0)) with a number of infected individuals ({I}_{0}) that is consistent with the ascertainment ratio in Italy during the early pandemic phase (3% by March 8, 2020 [26]; 10% was considered for sensitivity analysis), and the consolidated number of ascertained cases developing symptoms before strict restrictions were imposed on the general population (namely, 517 individuals on February 23, 2020). The dynamic model considered in this work is deterministic. However, initial infections are distributed over the national territory by random sampling from a multinomial distribution with probabilities proportional to the cumulative number of symptomatic cases retrospectively identified in Italy across the different municipalities as of February 15, 2020. To explore the uncertainty characterizing the initial spatial dispersal of SARS-CoV-2 infections, model simulations are repeated 100 times by randomly sampling the municipalities of residence of infectious individuals at the start of simulations. Results are presented both in terms of model mean estimates and 95% Prediction Intervals (PI) associated with different initial conditions, and in terms of model estimates associated with initial conditions minimizing the root mean square error between the time series of cases retrospectively identified at the regional level and those estimated by simulating the dynamic SIR model.

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