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Quantitative Methods for Investigating Infectious Disease Outbreaks

Ping Yan and Gerardo Chowell
Publication Date: 
Number of Pages: 
Texts in Applied Mathematics
[Reviewed by
Gilbert Gonzalez Parra
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This book on epidemiology is co-written by one of the world’s top experts on the subject. With the current Covid-19 pandemic the book can be very useful and timely for many interested readers. It includes an explanation of the main assumptions that are used for the current epidemic models that have been used to understand and analyze the Covid-19 pandemic. Thus, readers can think about potential risks of wrong assumptions regarding the prediction and forecasting of the outcomes of the pandemic. We can see that with more than 650,000 deaths related to the Covid-19 pandemic, this topic is of paramount importance for public health in a broad sense.
This book has nine chapters devoted to different aspects related to mathematical modeling of epidemics, with emphasis on quantitative methods to measure the impact of epidemic outbreaks on the population. The authors present how to compute under different scenario assumptions some key characteristics such as the timing of the peak of the prevalence, final epidemic size, and the well-known reproduction number R0. The authors offer highly technical aspects that allow a better understanding of the main epidemic outbreak outcomes. In addition, they refer to other relevant works that cover more specifically some particular results. Overall, the book allows the reader to grasp and analyze epidemic models and their key outcomes.
One important and interesting approach that the authors use as a main tool throughout the book is the  Laplace transform to compute different quantities related to the epidemic such as the fractions of infectious that will recover, or the mean infectious period. This particular approach is different from classical ones but allows in a clever way to generalize many results related to the epidemics under different scenarios. For instance, the authors vary the probability distribution functions of the infection duration and observe how the epidemic outcomes change. The authors also use in a suitable way the stochastic and hazard rate order to compare quantities.
In the book, the authors compare frequently the outcomes of stochastic and deterministic models, which enriches the discussion about theoretical results and real-world situations. One important aspect that the authors introduce in the book is the use of the convex order, which helps to analyze the impact of variability on different epidemiological metrics.
The authors present many illustrative examples where the effects of different probability distributions and survival and hazard functions can be observed. Thus, the interested reader can understand better the impacts of some particular model assumptions on the epidemic outcomes. These examples in many cases include a graph that has an ensemble of numerical simulations varying important epidemiological parameters, which allows seeing the impact of the parameters on the dynamics of the epidemic.
The book has at the end of each chapter a section devoted to proposed problems that allow the interested readers or graduate students to grasp better the particular content of the chapter. These problems are interesting and complement the ideas and material of the book.
This book can be used as a textbook for graduate courses. It requires knowledge in statistics, especially some topics as survival and hazard functions. Furthermore, the student will need some knowledge about calculus, ordinary differential equations and Laplace transforms. For general readers interested in the topic it is a good detailed book, but not at a beginner’s level. However, the general reader can grasp some important epidemic outcomes without reading in detail the calculations behind the results. The book has exercises of different levels of difficulty, and some can be extended for student projects. Thus, this book can be useful for graduate students, and researchers involved in mathematical epidemiology.


Dr. Gilberto Gonzalez-Parra is currently assistant professor at New Mexico Tech. His areas of research include developing, and analyzing mathematical models of infectious diseases.