The scope of applied mathematics reaches from the statement of the application problem over the development of a mathematical model to the corresponding analysis and numerical simulation. This book is an important contribution to demonstrate this approach. In the book, multiscale modeling of pedestrian dynamics is considered. The authors call the development of the model the “mathematization of reality”. The models are derived from basic principles about behavioral rules and self-organization. As indicated in the title, models on several scales are considered. Microscopic models consider the movement of each individual (the “particles”) in detail. In contrast to this, on the macroscopic scale a model for the development of the density of the particles is developed. The origins of models on the mesoscopic scale go back to the kinetic theory of gases by Ludwig Boltzmann. In the mesoscopic scale the statistical distribution of the states of the microscopic particles is considered.
The first part of the book is an introduction to the phenomena of crowd dynamics. In the second part the different types of mathematical models are studied. In particular, multiscale models are stated that interpolate between the microscopic and the macroscopic scale.
The book is very well-written and contains many excellent illustrations. It is both a valuable introduction to the modeling of pedestrian dynamics and to the methods of multiscale modeling.