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

Autorentext

Bouchra Aylaj is an Associate Professor with Habilitation in mathematics at University of Hassan II of Casablanca, Faculty Ain Chock, Morocco. She started her career in 2006 when she was called to develop a research program on mathematical modelling in biology. Her scientific activity has been focused on the following topics: scientific computing and control for risk analysis and analytical and computational problems in epidemiology. Subsequently, she moved her scientific interests to the modeling and related safety problems focused on social behaviors in human crowds.Nicola Bellomo is a distinguished professor at the University of Granada and Professor Emeritus at the Polytechnic University of Torino. He started his career in 1980 when he was called to cover the chair of mathematical physics and applied mathematics due to his scientific achievements on the mathematical theory of the Boltzmann equation and of stochastic differential equations. Subsequently, he moved his scientificinterests to the study of living systems, becoming one of the pioneers of the development of active particles methods to the modeling of large systems of self-propelled interacting entities. He is author of two books published by Birkhauser devoted to this topic. In 2009, he delivered the prestigious Shank Lecture on the modeling of immune competition, and was awarded the "Third Level Honor" in 2016 for scientific merits by the President of the Italian Republic.Livio Gibelli is a Lecturer in Mechanical Engineering at the University of Edinburgh. He received his Ph.D. in applied mathematics from the Politecnico di Milano and, prior to the current position, he worked as Research Fellow at the University of Warwick, Politecnico di Milano, Politecnico di Torino, and University of British Columbia. His main research interests include non-equilibrium multiphase fluid flows, the continuum description of slightly rarefied gases, the numerical methods for solving kinetic equations,and the modeling of crowd dynamics.Damian Knopoff is a chemical engineer and mathematician, holding a Ph.D. in Mathematics from Cordoba National University. Currently, he is an Associate Researcher at the Argentinian Scientific and Technical Research Council. His main research fields include nonlinear dynamical systems and numerical methods for differential equations with applications to the modeling and simulation of complex living systems, including biological phenomena, socio-economic systems, and crowd dynamics.

Klappentext

Using tools from mathematical kinetic theory and stochastic game theory, this work deals with the modeling of large complex systems in the applied sciences, particularly those comprised of several interacting individuals whose dynamics follow rules determined by some organized, or even "intelligent" ability. Traditionally, methods of mathematical kinetic theory have been applied to model the evolution of large systems of interacting classical or quantum particles. This book, on the other hand, examines the modeling of living systems as opposed to inert systems.

The author develops new mathematical methods and toolshopefully a "new" mathematicstoward the modeling of living systems. Such tools need to be far more complex than those dealing with systems of inert matter. The first part of the book deals with deriving general evolution equations that can be customized to particular systems of interest in the applied sciences. The second part of the book deals with various models and applications.

The presentation unfolds using the following common approach in each chapter:

• Phenomenological interpretation of the physical system in the context of mathematical modeling

• Derivation of the mathematical model using methods from mathematical kinetic theory for active particles

• Simulations, parameter sensitivity analysis, and critical inspection of the derived model towards validation

• Overview of presented ideas to improve existing models, with special emphasis on applications

Specific topics covered include:

• Modeling of the competition between cells of an aggressive invasive agent and cells of the immune system

• Modeling of vehicular traffic flow

• Modeling of swarms and crowd dynamics in complex geometric environments

• Methodological aspects related to multiscale modeling of large systems viewed as interconnected subsystems

Modeling Complex LivingSystems is a valuable resource for applied mathematicians, engineers, physicists, biologists, economists, and graduate students involved in modeling complex social systems and living matter in general.

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.