[Paper Review] Preliminary analysis of COVID-19 spread in Italy with an adaptive SEIRD model

Elena Loli Piccolomini, Fabiana Zama|arXiv (Cornell University)|Mar 22, 2020

COVID-19 epidemiological studies6 references44 citations

TL;DR

The paper introduces an adaptive SEIRD model with a time-dependent infection rate to analyze and forecast COVID-19 spread in Italian regions, calibrating on Lombardia, Veneto, and Emilia Romagna using Protezione Civile data and showing improved fit with a time-varying infection rate.

ABSTRACT

In this paper we propose a Susceptible-Infected-Exposed-Recovered-Dead (SEIRD) differential model for the analysis and forecast of the COVID-19 spread in some regions of Italy, using the data from the Italian Protezione Civile from February 24th 2020. In this study investigate an adaptation of the model. Since several restricting measures have been imposed by the Italian government at different times, starting from March 8th 2020, we propose a modification of SEIRD by introducing a time dependent transmitting rate. In the numerical results we report the maximum infection spread for the three Italian regions firstly affected by the COVID-19 outbreak(Lombardia, Veneto and Emilia Romagna). This approach will be successively extended to other Italian regions, as soon as more data will be available.

Motivation & Objective

• Develop a deterministic SEIRD framework to model COVID-19 spread in Italian regions.
• Incorporate time-dependent infection rate to reflect lockdown measures starting March 8, 2020.
• Calibrate model parameters against regional data and assess predictive capability.
• Compare standard SEIRD with an adaptive SEIRD(rm) to improve data fitting.

Proposed method

• Use SEIRD and SEIRD(rm) differential systems with five compartments: Susceptible, Exposed, Infected, Recovered, Dead.
• Partition the time interval into pre- and post-restriction periods with a decreasing time-dependent infection rate beta(t).
• Represent beta(t) as a piecewise decreasing rational function to capture policy changes: beta(t)=beta0 for t<t0, and beta0(1-ρ(t-t0)/t) for t>=t0, with ρ set to 0.75.
• Calibrate parameters via non-linear least squares with positivity constraints using lsqnonlin (trust-region) in Matlab.
• Solve the ODE system with initial conditions S(0)=N, E(0)=I(0)=I_init, R(0)=D(0)=0 and project up to 240 days.
• Evaluate fits on Lombardia, Veneto, and Emilia Romagna using datasets up to 20 March 2020.

Experimental results

Research questions

• RQ1 Can a SEIRD model with a time-dependent infection rate accurately capture the impact of lockdown measures in Italian regions?
• RQ2 Does the adaptive SEIRD(rm) provide a better fit and more reliable forecasts than the standard SEIRD when calibrated on regional data?
• RQ3 What are the estimated parameter values (β, α, γR, γD) and the time-varying reproduction rate Rt for each region?
• RQ4 How do peak infection, recovery, and death timings differ across Lombardia, Emilia Romagna, and Veneto under the adaptive modeling approach?

Key findings

• SEIRD parameter fits vary by region and data window; a time-dependent beta(t) improves alignment with observed IRD trajectories.
• In Lombardia, the SEIRD model estimates indicative peak timings and parameter values such as β≈0.3, α≈3, γR≈0.06, γD≈0.04 (illustrative from the reported results).
• The SEIRD(rm) model, with beta(t) decreasing after t0, reproduces data trends more precisely than SEIRD in the studied regions.
• Rt, defined as β(t)/(γR+γD), is shown as a time-varying function and decreases after lockdowns, reflecting policy impact.
• For Lombardia and Emilia Romagna, peaks for Infected occur around June 20th, while Veneto’s peak occurs later (around August 1st) due to differing testing policies.
• SEIRD(rm) yields region-specific peak values and emphasizes that undocumented infections may influence spread, consistent with cited literature.