What this research found
Italy's first COVID-19 wave was reconstructed from public daily case reports covering February 24 to May 31, 2020 — 98 days and 232,585 confirmed cases — then analyzed two ways: a Bayesian renewal-equation estimate of the instantaneous reproduction number Rt, and a fit of the classical SIR compartmental model. Rt peaked at 3.23 on March 3 and fell decisively below 1 on April 1, about three weeks after the March 9 national lockdown. The SIR fit, by contrast, returned an implausible basic reproduction number of 0.99 and missed the observed case peak by 31 days, a failure traced to the model's structure rather than to the optimizer.
- Transmissibility peaked at a posterior mean Rt of 3.23 on March 3, 2020 (95% credible interval 3.09 to 3.37), consistent with published Italian first-wave estimates in the 2.5 to 3.5 range.
- Rt first fell below the epidemic threshold of 1 on April 1, 2020 (posterior mean 0.978, 95% credible interval 0.968 to 0.988). The upper credible bound crossed on the same day, making the transition decisive rather than marginal, and suppression then held with Rt near 0.79 through late May (0.793 on May 31).
- The closed constant-transmission SIR model fitted a transmission rate of 0.329 per day and a recovery rate of 0.333 per day, giving a basic reproduction number of 0.99, and placed its predicted incidence peak 31 days before the observed peak of March 26.
- That failure is structural rather than numerical. The 232,585 confirmed cases amount to only about 0.39% of Italy's 60.3 million people, so susceptible depletion is negligible and a closed constant-parameter model cannot generate an interior peak that was in reality produced by lockdown rather than herd immunity.
- Curation caught a reporting artifact that would have corrupted both analyses: the source served 2020 figures as weekly aggregates, with only 14 of 98 days carrying a non-zero value. Taken literally that implies a false daily peak of 38,894 cases; redistributing each weekly total across the seven days it covers preserved the weekly and cumulative sums exactly and yielded a peak near 5,557 cases per day in late March.
How it was done
Daily case counts for Italy came from the Our World in Data COVID-19 compilation, filtered to the 98-day first-wave window and reindexed onto a complete daily calendar. Rt was estimated with the Cori renewal-equation method using a Gamma serial interval of mean 4.8 days and standard deviation 2.3 days (shape 4.355, scale 1.102) discretized over 30 days, a 7-day sliding window, and a weakly informative Gamma prior with mean and standard deviation of 5, producing 92 daily posterior estimates from March 1 to May 31. Separately, a deterministic SIR system on a closed population of 60,300,000 was integrated with an adaptive Runge-Kutta solver and fitted by differential evolution followed by a bounded local polish, minimizing squared error against daily incidence defined as the outflow from the susceptible compartment rather than infectious prevalence. Both the reconstructed daily series and a 7-day centered rolling average were fitted independently, and the work was written up as a 28-page technical report with runnable code.
Data sources
- Our World in Data COVID-19 dataset — Italy daily confirmed cases, February 24 to May 31, 2020 (98 days, 232,585 cases), snapshot accessed July 10, 2026
- Cori et al., American Journal of Epidemiology 178:1505 (2013) — renewal-equation framework for time-varying reproduction numbers
- ISTAT and Ministry of Health national SARS-CoV-2 seroprevalence survey, May to July 2020 — about 2.5% IgG seroprevalence, roughly 1.48 million past infections
- Riccardo et al., Eurosurveillance 25:2000790 (2020) and Cereda et al., Epidemics 37:100528 (2021) — published Italian first-wave reproduction number estimates
Limitations
Daily incidence had to be reconstructed from weekly aggregates by uniform redistribution, so the within-week shape of the curve is imposed rather than observed, and the serial interval was fixed at one published estimate when alternatives range from roughly 4 to 6.6 days. Both estimates rest on confirmed cases, which captured only a fraction of true infections in early 2020, and the compartmental model was deliberately restricted to constant parameters and a fixed population size, so its basic reproduction number is diagnostic rather than authoritative.
How this research was produced
K-Dense Web planned and ran this epidemiology investigation end to end — gathering the sources, carrying out the analysis, producing the figures, and drafting the report. The full session transcript, including every intermediate step, is available to view.
