A model predictive control approach to optimally devise a two-dose vaccination rollout: A case study on COVID-19 in Italy

The COVID-19 pandemic has led to the unprecedented challenge of devising massive vaccination rollouts, toward slowing down and eventually extinguishing the diffusion of the virus. The two-dose vaccination procedure, speed requirements, and the scarcity of doses, suitable spaces, and personnel, make the optimal design of such rollouts a complex problem. Mathematical modeling, which has already proved to be determinant in the early phases of the pandemic, can again be a powerful tool to assist public health authorities in optimally planning the vaccination rollout. Here, we propose a novel epidemic model tailored to COVID-19, which includes the effect of nonpharmaceutical interventions and a concurrent two-dose vaccination campaign. Then, we leverage nonlinear model predictive control to devise optimal scheduling of first and second doses, accounting both for the healthcare needs and for the socio-economic costs associated with the epidemics. We calibrate our model to the 2021 COVID-19 vaccination campaign in Italy. Specifically, once identified the epidemic parameters from officially reported data, we numerically assess the effectiveness of the obtained optimal vaccination rollouts for the two most used vaccines. Determining the optimal vaccination strategy is nontrivial, as it depends on the efficacy and duration of the first-dose partial immunization, whereby the prioritization of first doses and the delay of second doses may be effective for vaccines with sufficiently strong first-dose immunization. Our model and optimization approach provide a flexible tool that can be adopted to help devise the current COVID-19 vaccination campaign, and increase preparedness for future epidemics.