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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 In addition, an unpublished SIR-type mathematical model with three delays is proposed as a main contribution.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]

In this paper, a non-linear multivariable mathematical model of a pump storage hydroelectric power plant, developed in Matlab-Simulink, is used to evaluate the performance of a Proportional Integral Derivative (pseudo derivative) controller with anti-windup, where the integral and derivative actions are of fractional order. This control is robust, maintaining its performance in the case of direct response and in the case of cross coupling response. Similarly, the advantage of using a filter to reduce the cross-coupling interaction of this system is shown. The effect of this filter, of fractional order, on the performance of the system, is shown by reducing the integral of the squared error. [ABSTRACT FROM AUTHOR]