Modeling, Estimation, and Optimal Control of Anti-COVID-19 Multi-dose Vaccine Administration

The recent trends of the COVID-19 research are being devoted to disease transmission modeling in presence of vaccinated individuals, while the emerging needs are being focused on developing effective strategies for the optimal distribution of vaccine between population. In this context, we propose a novel non-linear time-varying model that effectively supports policy-makers in predicting and analyzing the dynamics of COVID-19 when partially and fully immune individuals are included in the population. Differently from the related literature, where the common strategies typically rely on the prioritization of the different classes of individuals, we propose a novel Model Predictive Control approach to optimally control the multi-dose vaccine administration in the case the available number of doses is not sufficient to cover the whole population. Focusing on the minimization of the expected number of deaths, the approach discriminates between the number of first and second doses. We calibrate the model on the Israeli scenario using real data and we estimate the impact of the vaccine administration on the virus dynamics. Lastly, we assess the impact of the first dose of the Pfizer's vaccine confirming the results of clinical tests.