A Quest Towards a Mathematical Theory of Living Systems

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This monograph lays the groundwork for a unified mathematical approach to modeling and analyzing large, complex systems of interacting living entities. Drawing on two decades of interdisciplinary research, it examines how mathematical kinetic theory and evolutionary game theory can illuminate the dynamics of living systems. The authors aim to contribute new tools and strategies, potentially leading to a novel mathematical theory. The first chapter outlines key features of living systems and proposes a modeling strategy. Subsequent chapters delve into necessary methods for practical application. Chapter Two introduces mathematical kinetic theory, focusing on the Boltzmann equation, the Enskog equation, mean field models, and Monte Carlo methods. Chapter Three utilizes evolutionary game theory to derive mathematical structures that capture the complexity of interactions in living systems. The book also explores relevant applications for developing specific models, including social systems in Chapter Five and crowd dynamics in Chapter Six, illustrating the modeling of multicellular systems. The final chapter discusses additional applications and presents open problems, alongside the authors' speculations on potential paths toward a mathematical theory of living systems. This unique contribution is poised to significantly influence future research in the field, appealing to mathematical biologists, systems biologists, biophysicist