The geography of COVID-19 spread in Italy and implications for the relaxation of confinement measures

The study addresses how Italy can safely relax COVID-19 confinement measures while avoiding resurgence. Because SARS-CoV-2 transmission includes substantial inapparent (asymptomatic and pre-symptomatic) infections and exhibits marked spatial heterogeneity across Italy, national-level, spatially explicit models are needed to inform policy. The authors adopt and update a province-resolved (107 provinces) epidemiological model to: (i) project the baseline epidemic trajectory under continued lockdown, (ii) quantify deviations from baseline associated with increased transmission following relaxation, and (iii) estimate the daily isolation effort required to counterbalance such increases. The context includes under-reporting of infections, variability in data quality, and evolving non-pharmaceutical interventions (mobility restrictions, social distancing, PPE, testing and tracing). The central research questions are how much transmission can increase without triggering a rebound, and what levels of targeted isolation are sufficient to maintain a decreasing epidemic trajectory after reopening.

The paper builds on evidence that a large fraction of SARS-CoV-2 transmission arises from inapparent infections (asymptomatic and pre-symptomatic), with pre-symptomatic transmission potentially exceeding that from symptomatic and asymptomatic cases. It references early modeling for single cities and countries, highlighting the need for spatially explicit approaches that capture geographic heterogeneity and mobility networks. The work is situated among studies on the impact of non-pharmaceutical interventions, the role of testing and contact tracing in mitigating second waves, and empirical findings on viral shedding dynamics and mask efficacy. It also acknowledges limitations of reported case and death data due to under-reporting and testing variability, motivating the use of reconstructed hospitalization flows for calibration.

Model: A spatially explicit SEPIA compartmental ODE model is implemented for each of 107 Italian provinces. Compartments include susceptible (S), exposed/latent (E), peak infectivity (P), heavily symptomatic infectious (I), asymptomatic/mildly symptomatic infectious (A), hospitalized (H), quarantined at home (Q), recovered (R), and dead (D). Transmission is frequency-dependent, with force of infection in each province depending on local and connected provinces via mobility-derived contact probabilities. Infectious stages contributing to transmission are P, I, and A, with stage-specific transmission rates βP, βI, βA. Spatial coupling: Mobility/contact structure is parameterized using ISTAT 2011 commuter data. For each province i, the fraction of mobile people (pi) and their distribution across destinations (qij) inform contact probabilities Cij, accounting for contacts at home province and during travel, differentiated by epidemiological compartment via parameters rX. Data: Calibration uses reconstructed daily hospital admissions at provincial level, derived from national data (Protezione Civile) on hospital occupancy, deaths, and discharges. Discharge and death delays are modeled as gamma distributions (death delay mean 7 days, CV 0.5; discharge delay mean 14 days, CV 0.5). The median over 100 stochastic reconstructions is downscaled to provinces and smoothed (7-day moving average). Parameterization and estimation: Time-varying transmission reflects phased interventions. Four βP levels are used: βP0 (pre-Feb 24), βP1 (post-Feb 24), βP2 (post-Mar 8), and a linear decrease Mar 10–Mar 22 to a post-lockdown level βP,f held constant. βI and βA are proportional to βP (ratios estimated or fixed as per Table 1). Province-specific post-lockdown transmission reductions are modeled via a hierarchical Bayesian framework with truncated Gaussian priors on βP,f/βP0. Initial conditions include one exposed case in Lodi A0 days before Feb 24 and province-specific seeding in E to account for early spread. Likelihood assumes negative binomial (NB1) observation model with mean equal to modeled hospital admissions and variance ωμ. Priors are uninformative within biologically plausible bounds; DREAMzs MCMC is used for posterior sampling. Sensitivity analyses consider different heavy symptomatic fractions σ = 10%, 25% (reference), 50% and fast waning immunity (3 months), which had negligible effect within the simulation horizon. Scenarios: Post-May 4 relaxation is represented as multiplicative increases in effective transmission (+20% and +40%) relative to lockdown transmission to explore impacts on daily hospitalizations at regional and national scales. Isolation intervention modeling: To offset increased transmission, isolation is targeted to E and P compartments, reflecting evidence that ~86% of infections occur from individuals at peak infectivity and that shedding peaks near symptom onset. Isolation is implemented as additional outflows ρE·E and ρP·P (assumed equal: ρE=ρP=ρ), removing individuals from community transmission. For each province/region, the daily percentage ρ and absolute number ρ(E+P) required to maintain the baseline decreasing trajectory are estimated across σ values. Feasibility is compared to the theoretical capacity obtained by tracing and isolating all infections generated by new daily symptomatic cases (primary contacts). Timing sensitivity is assessed by delaying relaxation by one month. Ex-post assessment: Parameters are re-estimated using data up to June 17, 2020, adding a parameter βP,post to capture transmission after May 4 (allowing regional variation) and updating βP,f estimates for late-lockdown. Comparisons between projected baseline scenarios and realized trajectories quantify changes in transmission by region.

- Model fit: The spatial model accurately reproduces cumulative and daily hospitalizations across 107 provinces up to May 1, 2020. - Transmission reduction: Effective transmission during lockdown decreased to 30–40% of the initial uncontrolled level, implying an approximate 60–70% reduction. This reduction is largely due to interventions rather than acquired immunity. - Scenario outcomes: If lockdown-era transmission persists, daily hospitalizations continue to decline in all regions (baseline). A +20% increase in transmission yields a slower decline; a +40% increase produces a pronounced rebound in most regions. - Susceptibility and herd immunity: As of May 1, the susceptible fraction remained high, especially outside northern regions. In Lombardia, the susceptible fraction was approximately 0.97 (σ=50%), 0.95 (σ=25%), and 0.87 (σ=10%), indicating herd immunity is far from being reached. - Infection fatality rate estimates: IFR was estimated at ~4% (σ=50%), ~2% (σ=25%), and ~0.8% (σ=10%). - Isolation targets: To counter a +40% increase in transmission in Lombardia (σ=25%), isolating approximately 1,200 of ~22,000 E+P individuals per day (~5.5%) would maintain the baseline decreasing trend. The required isolation percentage is relatively insensitive to σ, but the absolute numbers increase as σ decreases due to a larger unobserved epidemic. Tracing and isolating only primary contacts of new symptomatic cases may suffice for mild increases; for larger increases or lower σ, secondary contacts must also be targeted. - Timing effect: Delaying relaxation by one month would reduce E+P prevalence by about two-thirds, proportionally lowering the absolute isolation effort needed. - Ex-post findings (to June 17): Nationally, observed hospitalizations are slightly below the baseline projection. Most regions show decreased transmission post-relaxation compared to late lockdown. Notable estimates of change in transmission (median, with 95% CI): Lombardia +8% (+6%, +11%); Piemonte −22% (−26%, −18%); Veneto −23% (−31%, −15%); Emilia Romagna −20% (−26%, −14%); Marche −27% (−39%, −15%); Sardegna −55% (−72%, −36%). Lombardia stands out as increasing despite overall declines elsewhere.

The findings show that Italy’s NPIs—social distancing, mobility restrictions, PPE, and behavioral adaptations—reduced transmission by roughly two-thirds during lockdown, with minimal contribution from acquired immunity, underscoring the risk of resurgence upon relaxation. Scenario analyses quantify thresholds: moderate increases in transmission can be managed without rebound, while larger increases (≈+40%) likely trigger renewed growth absent additional controls. A targeted isolation strategy focused on pre-symptomatic and early infectious individuals (E and P) can compensate for increased contact rates, provided sufficient tracing and testing capacity. Regional heterogeneity in both achieved transmission reduction and susceptibility necessitates geographically tailored responses; for example, regions like Piemonte are more prone to rebound under the same increase compared to Lombardia at lockdown’s end due to differing effective transmission at that point. Real-time monitoring of deviations from a modeled baseline is advocated, potentially via data assimilation (e.g., ensemble Kalman filtering), to infer realized transmission and adjust interventions promptly. The ex-post assessment indicates that partial, protocol-driven reopening and enhanced masking/tracing likely maintained or further reduced transmission in most regions, except Lombardia, highlighting the importance of sustained contact tracing capacity when case numbers remain higher. Potential contributors to post-lockdown dynamics include continued restrictions, mask mandates, improved outbreak control in healthcare/long-term care settings, possible seasonality, and local stochastic fade-outs, though the latter is not captured by the deterministic model.

This work presents a province-resolved, mobility-informed modeling framework that captures the geography of COVID-19 transmission in Italy and provides actionable scenario analyses for reopening. It quantifies how much transmission can increase without causing resurgence, and specifies isolation targets—especially for pre-symptomatic and early infectious individuals—to maintain declining trends after relaxation. Ex-post evaluation confirms that, in most regions, transmission did not increase following May 4 reopening, suggesting that a mix of continued NPIs, masking, and improved tracing/isolation can enable safer relaxation. Policy implications include the need for region-specific strategies calibrated to local transmission and susceptibility, scaling tracing/testing to meet isolation targets, and readiness to adjust measures if monitored trajectories deviate from baseline. Future research should integrate real-time data assimilation for adaptive control, incorporate stochastic effects at low incidence, refine estimates with richer contact tracing data, assess seasonality and waning immunity impacts over longer horizons, and update mobility/contact structures with contemporaneous data.

- Data limitations: Confirmed cases and even deaths are under-reported; calibration relies on reconstructed hospital admissions using assumed delay distributions, introducing uncertainty. - Model assumptions: No importation from outside Italy; homogeneous mixing within provinces; deterministic continuous ODE framework does not capture stochastic fade-out at low incidence; immunity assumed durable over the study horizon (with a sensitivity check for rapid waning showing minimal short-term impact). - Parameter uncertainty: Results depend on the heavy symptomatic fraction σ; IFR and susceptible fractions vary accordingly. Some transmission parameters are estimated with regional heterogeneity but within model constraints. - Unmodeled factors: Seasonality not explicitly modeled; no explicit age structure; limited granularity on healthcare and long-term care facility outbreaks; tracing/testing processes are abstracted as effective isolation rates without operational constraints. - Mobility data: Spatial coupling based on 2011 ISTAT commuter data, which may not fully represent mobility patterns during the pandemic beyond reductions captured by transmission parameter changes.