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Humanity has suffered throughout its history from different types of pandemics caused by deadly infectious diseases. Mathematical models are very useful tools to understand the dynamics of the behavior and propagation of these. Among these models are those known as SIS, SIR and SEIR. This paper presents a brief explanation of the structure of these models and its use in some pandemics. In particular, some SIR-type models without and with delays are analyzed with special interest, as well as their applications to the current pandemic caused by the SARS-CoV-2 virus. To determine the correspondence between some of the models analyzed and the data of Infectious and Recovered from Mexico reported by the World Health Organization (WHO), simulations are presented in three different time periods between the years 2020-2021. In addition, an unpublished SIR-type mathematical model with three delays is proposed as a main contribution. Finally, a discussion is given on the application of numerical algorithms to identify some parameters of mathematical models, such as ordinary least squares. [ABSTRACT FROM AUTHOR]