The COVID-19 pandemic that emerged in 2020 has highlighted the complex interplay between vaccine hesitancy and societal polarization. In this study, we analyse the dynamical polarization within a social network as well as the network properties before and after a vaccine was made available. Our results show that as the network evolves from a less structured state to one with more clustered communities. Then using an agent-based modeling approach, we simulate the propagation of a virus in a polarized society by assigning vaccines to pro-vaccine individuals and none to the anti-vaccine individuals. We compare this propagation to the case where the same number of vaccines is distributed homogeneously across the population. In polarized networks, we observe a significantly more widespread diffusion of the virus, highlighting the importance of considering polarization for epidemic forecasting.