Mathematical Modeling of Complex Biological Systems

This book develops methods using mathematical kinetic theory to describe the evolution of several socio-biological systems. Specifically, it deals with modeling and simulations of biological systems constituted by large populations of interacting cells, whose dynamics follow both the rules of mechanics as well as their own ability to organize movement and biological functions. Proposed is a new biological model focused on the analysis of competition between cells of an aggressive host and cells of the immune system. Modeling in kinetic theory may represent a way to understand phenomena of nonequilibrium statistical mechanics that is not described by the traditional macroscopic approach. The authors of this work focus on models that refer to the Boltzmann equation (generalized Boltzmann models) with the dynamics of populations of several interacting individuals (kinetic population models). The book follows the classical research line applied to modeling real systems, linking the phenomenological observation of systems to modeling and simulations. Computational algorithms are applied and qualitative analysis techniques are used to identify the prediction ability of specific models. The book will be a valuable resource for applied mathematicians as well as researchers in the field of biological sciences. It may also be used for advanced graduate courses in biological systems modeling with applications to collective social behavior, immunology, and epidemiology.