Abstract
From the beginning of the SARS-CoV-2 pandemic, mathematical models have been developed to describe, predict, and control its evolution. This chapter presents a set of useful mathematical tools to understand the epidemic dynamics. First, to obtain a rough approximation to the magnitude of the epidemic, the basic and effective reproduction numbers are estimated. Then, several growth models are applied to estimate the peak and final size of the epidemic. The results show that mitigation measures were able to flatten the epidemic curve, at the cost of extending it more than expected. Nonetheless, these heuristic models have limitations. Thus a mechanistic Kermack-McKendrick model is used to explore transmission and superspreading events. Our results show that these events can delay the peak incidence or drive the epidemic into a long plateau with relatively constant but high incidence. This highlights the need to monitor and anticipate atypical mobility events. Also, our projections of the pandemic trend for the last part of 2020 and the beginning of 2021, show that temporary immunity and an increase in the effective contact rate may generate an epidemic rebound by the end of 2020. Data from Mexico is used to exemplify the estimation and limitations of all the models. Although Mexico is our case study, the methodology can be extended to other regions.