at Google ScholarTitle data
Melhani, Lokman Rachid ; Sferlazza, Antonino ; Grüne, Lars ; Adorno, Dominique Persano ; D'Ippolito, Filippo ; Santangelo, Omar Enzo ; Marchese, Ivan ; Lo Burgio, Antonino ; Firenze, Alberto:
A Nine-Compartment Nonlinear Epidemic Model with Spline-Based Identification of Time-Varying Transmission and Vaccination Dynamics : Application to the COVID-19 Third Wave in Italy.
Bayreuth ; Palermo
,
2026
. - 23 p.
DOI: https://doi.org/10.48550/arXiv.2606.07413
Abstract in another language
We develop a nine-compartment nonlinear epidemic model incorporating two co-circulating viral strains (ancestral I1 and the Alpha variant B.1.1.7 I2, which is 43-90% more transmissible, c2=1.5), a super-spreader subpopulation, partial vaccine-induced immunity with waning, and explicit hospitalization dynamics with differentiated mortality. Transmission and vaccination rates are treated as time-varying control inputs and identified from Italian COVID-19 data (January-May 2021) via a Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) control-node parameterization, reducing calibration to a fourteen-variable Sequential Quadratic Programming (SQP) problem with monotonicity and box constraints. A parametric bootstrap (n=1000) quantifies parameter uncertainty. The calibrated model achieves R^2=0.966 for active hospitalizations, R^2=0.987 for cumulative fatalities, and R^2=0.999 for cumulative vaccinations. Well-posedness, the basic reproduction number in closed form, and local and global stability of the disease-free equilibrium are established analytically. An L-infinity approximation error bound shows that the PCHIP control-node parameterization converges to the true time-varying parameters at rate O(h^2) as the node spacing vanishes. Local identifiability and a noise stability bound are established via the Fisher information matrix. A sufficient threshold condition proves epidemic decay under time-varying suppression whenever the effective reproduction number remains persistently below one. Sensitivity analyses consistently rank hospital throughput parameters above the transmission rate, providing a mathematical basis for the observation that reactive containment measures cannot prevent a hospitalization peak already driven by the pre-existing latent viral load.