In this work, several mathematical models for the spread of viruses and diseases are presented. In particular, the work focuses on the coronavirus disease 2019 (COVID-19) pandemic. A multi-population model is presented for the study of the interaction of various populations and the contagion of the virus between them. A second model on vaccination is presented, which allows analyzing the behavior of the disease taking into account the effectiveness of the vaccine and the speed of COVID-19 after the vaccination process. Finally, both models are applied to analyze the epidemic in Cuba. For this study, the official data reported by the Cuban Ministry of Health from March 2020 to August 2021 is used.