The COVID-19 pandemic is not the first pandemic to have occurred in the history of humanity, but it is the first one where it is possible to use a vast array of mathematical tools to describe, analyze, and even attempt to forecast possible outcomes in time and space.
The tools that are discussed in this work are mostly statistical or based on statistical features. Even compartmental models like susceptible-exposed-infected-recovered (SEIR), which are sets of coupled nonlinear ordinary differential equations (ODEs), have to rely on parameters that come from statistics. The difference: SEIR and other compartmental models herein described are meant to study the phenomenological part of the pandemic.
Concerning the more statistical modeling, much is included: from the simplest linear regression, to sophisticated artificial intelligence (AI), to neural network approaches such as H2O AutoML, to ARIMA models, where it is concluded that autoregressive models integrated with the moving average can be considered as a fairly good prediction model. Arguably, in this book, the most successful predictions come from H2O AutoML, with an R2 better than 0.99. However, the implementation of simpler statistical tools do have their own (restricted) range of predictive power, and were used as a first approximation.
Most of the book discusses time series forecasting, but the last part of the text treats spatial statistics, in particular the geographical spread of the COVID-19 pandemic over some parts of Brazil for which 2D Kalman filters were used. Kalman filters were also used for the time series descriptions of some of the cases described throughout this work.
This book is still of great interest for mathematical modelers--it nicely summarizes many important tools, with concrete examples, that could be adapted for other situations. Thus, this work comes with solid pedagogical value, and as a form of reviewing some statistical and phenomenological methods for analyzing time series and spatial statistics.
Some material may even interest the pure mathematician, for example, the underlying inverse-problem setup that entails describing the behavior of the probability density functions of the (non-)fixed parameters of the compartmental models. I strongly recommend this book to advanced undergraduate engineers and mathematicians as well as specialists dealing with dynamical system modeling.