arXiv subjects

Alberto Firenze

Publications and source records attributed to Alberto Firenze.

3 recordsLinked to original sources

arXiv2026

Optimal Control of Pandemic Dynamics via Model Predictive Control: A Health-Economic Trade-off Analysis

This paper addresses the optimal control of epidemic dynamics under conflicting socio-economic objectives. We propose an economic Model Predictive Control (MPC) framework, applied to an extended SEIR-V (Susceptible-Exposed-Infected-Recovered-Vaccinated) compartmental model to govern the spread of an infectious disease while minimizing economic disruption. The control problem is formulated as a constrained nonlinear optimization problem, in which the controller dynamically adjusts social interaction levels (transmission rate beta) and vaccination efforts to minimize a composite cost function that penalizes fatalities, healthcare capacity violations, and economic losses. We conduct a rigorous sensitivity analysis of the prediction horizon N, demonstrating that the closed loop is robust to the horizon choice and that N = 35 days minimizes the realized cost. Furthermore, both the closed-loop solution and an open-loop turnpike analysis across diverse initial conditions reveal that the celebrated "Hammer and Dance" mitigation strategy emerges naturally as the mathematical optimum: the optimal trajectories anchor to a unique suppression turnpike (maximum lockdown) to drive hospitalizations toward the disease-free equilibrium before progressively reopening the economy. Through a turnpike-based argument we establish practical asymptotic stability of the optimal operating point, providing a mathematically grounded decision-support tool for pandemic policy.

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arXiv2026

Extended Kalman Filter-Based State Estimation for a Nine-Compartment Nonlinear Epidemic Model -- Convergence Analysis and In-Silico Benchmark Calibrated on the COVID-19 Third Wave in Italy

This paper addresses real-time state estimation for a nine-compartment nonlinear COVID-19 epidemic model with two co-circulating strains, a super-spreader subpopulation, vaccination with waning immunity, hospitalization, and mortality. Time-varying transmission and vaccination rates are known inputs from a companion calibration, leaving the reconstruction of all nine states from three routinely reported observables: hospitalizations H, fatalities F, and vaccinated stock V. The contributions are theoretical rather than in the filter recursion. First, a Lie-derivative observability analysis yields, via a six-step derivation, the closed-form determinant |det(O9)| = delta_w * gamma_a^2 * kappa * rho2 * w1^2 * (delta_i - delta_p)^2 * |r1 - r2|, showing the level-2 codistribution is rank-deficient at the calibrated symmetric parameters (delta_i = delta_p, r1 = r2); the third Lie derivative restores full rank 9, with r2 the symmetry-breaking parameter. Second, an EKF is designed on the Euler-discretized dynamics with a closed-form 9x9 Jacobian and Joseph covariance update. Third, local exponential mean-square boundedness of the error is proved as a full theorem via the Reif-Gunther-Yaz-Unbehauen hypotheses, exploiting the bilinear drift and linear output to obtain a global-radius quadratic remainder bound that extends to bilinear-drift, linear-output systems. Fourth, the noise covariances are designed from calibration residuals and assessed by NEES and innovation-whiteness tests. All experiments use synthetic measurements from the calibrated model, so reported RMSE values (0.07%-2.72%) are methodology benchmarks, not predictive accuracy. A parameter-mismatch study shows measured and directly-coupled channels stay accurate under model error up to +/-30% while indirectly observed states degrade gracefully. The framework provides the state-feedback basis for future Model Predictive Control.

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arXiv2026

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

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.

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