This book develops new mathematical methods and tools to model living systems. The material it presents can be used in such real-world applications as immunology, transportation engineering, and economics.

Thesubjectofthisbookisthemodelingofcomplex systemsinthelife sciences constituted by a large number of interacting entities called active particles. Their physical state includes, in addition to geometrical and mechanical variables, a variable called the activity, which characterizes the speci?c living system to be modeled. Interactions among particles not only modify the microscopic state, but may generate proliferative and/or destructive phenomena. The aim of the book is to develop mathematical methods and tools, even a new mathematics, for the modeling of living systems. The background idea is that the modeling of living systems requires technically complex mathematical methods, which may be s- stantially di?erent from those used to deal with inert matter. The?rstpart ofthe bookdiscussesmethodological issues, namely the derivation of various general mathematical frameworks suitable to model particular systems of interest in the applied sciences. The second part presents the various models and applications. The mathematical approach used in the book is based on mathema- cal kinetic theoryfor active particles, whichleads tothederivation of evo- tion equations for a one-particle distribution function over the microscopic state. Two types of equations, to be regarded as a general mathematical framework for deriving the models, are derived corresponding to short and long range interactions.

Unique book with respect to the existing literature; very little is available in the field using this particular approach Using new methods and tools from mathematical kinetic theory and stochastic game theory, this book examines the modeling of living systems as opposed to inert systems Real-world applications to immunology, transportation engineering, and economics Appeals to a broad audience: applied mathematicians, engineers, physicists, biologists, economists, and graduate students involved in modeling complex social systems and living matter in general Includes supplementary material: sn.pub/extras

Inhalt
From Scaling and Determinism to Kinetic Theory Representation.- Mathematical Structures of the Kinetic Theory for Active Particles.- Additional Mathematical Structures for Modeling Complex Systems.- Mathematical Frameworks.- Modeling of Social Dynamics and Economic Systems.- Mathematical Modeling.- Complex Biological Systems:.- Modeling Crowds and Swarms:Congested and Panic Flows.- Additional Concepts on the Modeling of Living Systems.