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 In addition, an unpublished SIR-type mathematical model with three delays is proposed as a main contribution.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

Background. One of the reasons to study infectious diseases is to increase their control and eradication. Mathematical models could be a powerful tool to achieve that end, which allows for optimization of limited resources, and conduct more effective measures; these models are made to predict and increase understanding of the studied phenomenon. The aim of this paper is to conduct simulations using the stochastic model known as Susceptible, Infected, Recovered (SIR), and introduce them in the curricula of students, epizootiological analyses, and decision-making. Methods. Virtually the entrance of ten migrating birds with respiratory processes was simulated on bird rearing farms averaging 5000 free-range poultry from different types. The R0 was determined depending on the incidence. Results. Simulation was run with a low communicability index (1.8 %), that is, 1.8 out of every 100 birds get sick, after interacting with other 5 birds each, at random, for 10 days. In the absence of intervention, there would be a spike of sick animals at 20 days, surpassing 3000 birds. A basic reproductive number greater than the unit (R0=1.14) was observed, thus qualifying as an epidemic outbreak. Conclusions. A number of simulations were made using the stochastic model with a sustainable analytical tool based on an R-free program. The need to integrate the epizootiology, epidemiology, and mathematic was demonstrated, suggesting that appropriate training should be provided by competent professionals. [ABSTRACT FROM AUTHOR]

The effect of non-pharmacological interventions to contain the spread of SARS-CoV-2 have caused negative impacts, especially in education. Re-opening schools and universities is regarded as a high risk scenario. This paper seeks to understand, with the help of mathematical modeling, possible mechanisms through which the virus could spread in an academic environment and to quantify contagions attributable to participating in academic activities. To simulate the dynamics of contagion at the University, an agent-based mathematical model that incorporated stochastic differential equations was built using academic data for the University's 2020-2 semester. The model suggests that hybrid-attendance combined with epidemiological surveillance can produce very safe operating conditions without significantly contributing towards more COVID infections in the city of Bogotá. [ABSTRACT FROM AUTHOR]