Because a fast vaccination rollout against coronavirus disease 2019 (COVID-19) is critical to restore daily life and avoid virus mutations, it is tempting to have a relaxed vaccination-administration management system. However, a rigorous management system can support the enforcement of preventive measures, and in turn, reduce incidence and deaths. Here, we model a trustable and reliable management system based on blockchain for vaccine distribution by extending the Susceptible-Exposed-Infected-Recovery (SEIR) model. The model includes prevention measures such as mask-wearing, social distancing, vaccination rate, and vaccination efficiency. It also considers negative social behavior, such as violations of social distance and attempts of using illegitimate vaccination proofs. By evaluating the model, we show that the proposed system can reduce up to 2.5 million cases and half a million deaths in the most demanding scenarios.