  Population-wide vaccination is critical for containing the SARS-CoV-2
(Covid-19) pandemic when combined with restrictive and prevention measures. In
this study, we introduce SAIVR, a mathematical model able to forecast the
Covid-19 epidemic evolution during the vaccination campaign. SAIVR extends the
widely used Susceptible-Infectious-Removed (SIR) model by considering the
Asymptomatic (A) and Vaccinated (V) compartments. The model contains several
parameters and initial conditions that are estimated by employing a
semi-supervised machine learning procedure. After training an unsupervised
neural network to solve the SAIVR differential equations, a supervised
framework then estimates the optimal conditions and parameters that best fit
recent infectious curves of 27 countries. Instructed by these results, we
performed an extensive study on the temporal evolution of the pandemic under
varying values of roll-out daily rates, vaccine efficacy, and a broad range of
societal vaccine hesitancy/denial levels. The concept of herd immunity is
questioned by studying future scenarios which involve different vaccination
efforts and more infectious Covid-19 variants.
