An Age-Structured Vaccination Strategy for Epidemic Containment: A Model Predictive Control Approach

Abstract

This work presents a novel Model Predictive Control (MPC) approach to develop an optimal age-structured vaccination strategy for the containment of COVID-19 in Wallonia, Belgium. The proposed MPC framework is designed to minimize deaths, achieve early disease eradication, and adhere to operational constraints. By incorporating an age-structured Susceptible-Infected-Recovered-Deceased (SIRD) model with an additional term for vaccination, the MPC strategy dynamically adapts to the evolving epidemic state. A detailed proof of the asymptotic stability and recursive feasibility of the proposed MPC algorithm is provided. This ensures that the optimal cost at each step provides an upper bound on the minimal number obtainable of deaths at the end of the pandemic. Moreover, simulations demonstrate that the proposed MPC approach outperforms the decreasing age vaccination strategy adopted by the Belgian government during the first wave of vaccinations. The results highlight the potential of MPC-based vaccination strategies to reduce the total number of deaths, accelerate disease eradication, and optimize vaccine administration.