This monograph has the ambitious aim of developing a mathematical theory of complex biological systems with special attention to the phenomena of ageing, degeneration and repair of biological tissues under individual self-repair actions that may have good potential in medical therapy. The approach to mathematically modeling biological systems needs to tackle the additional difficulties generated by the peculiarities of living matter. These include the lack of invariance principles, abilities to express strategies for individual fitness, heterogeneous behaviors, competition up to proliferative and/or destructive actions, mutations, learning ability, evolution and many others. Applied mathematicians in the field of living systems, especially biological systems, will appreciate the special class of integro-differential equations offered here for modeling at the molecular, celular and tissue scales. A unique perspective is also presented with a number of case studies in biological modeling.

This monograph has the ambitious aim of developing a mathematical theory of complex biological systems with special attention to the phenomena of ageing, degeneration and repair of biological tissues under individual self-repair actions that may have good potential in medical therapy. The approach to mathematically modeling biological systems needs to tackle the additional difficulties generated by the peculiarities of living matter. These include the lack of invariance principles, abilities to express strategies for individual fitness, heterogeneous behaviors, competition up to proliferative and/or destructive actions, mutations, learning ability, evolution and many others. Applied mathematicians in the field of living systems, especially biological systems, will appreciate the special class of integro-differential equations offered here for modeling at the molecular, cellular and tissue scales. A unique perspective is also presented with a number of case studies in biological modeling. Contents:Looking for a Mathematical Theory of Biological SystemsOn the Complexity of Biological SystemsImmune System, Wound Healing Process, and System Biology:The Immune System: A Phenomenological OverviewWound Healing Process and Organ RepairFrom Levels of Biological Organization to System BiologyMathematical Tools:Mathematical Tools and StructuresMultiscale Modeling: Linking Molecular, Cellular, and Tissues ScalesApplications and Research Perspectives:A Model for the Malign Keloid Formation and Immune System CompetitionMacroscopic Models of Chemotaxis by KTAP Asymptotic MethodsLooking Ahead Readership: Researchers in mathematical modeling and biological systems. Keywords:Mathematical Theory;Biological Systems;SubsystemKey Features:Provides a new conceptual background to applied mathematicians involved in the challenging research field of living systems, and specifically biology systemsGives more accurate ODE, cellular-automata, and continuum models from the biological point of view

This volume examines a variety of biological and medical problems using mathematical models to understand complex system dynamics. Featured topics include autism spectrum disorder, ectoparasites and allogrooming, argasid ticks dynamics, super-fast nematocyst firing, cancer-immune population dynamics, and the spread of disease through populations. Applications are investigated with mathematical models using a variety of techniques in ordinary and partial differential equations, difference equations, Markov-chain models, Monte-Carlo simulations, network theory, image analysis, and immersed boundary method. Each article offers a thorough explanation of the methodologies used and numerous tables and color illustrations to explain key results. This volume is suitable for graduate students and researchers interested in current applications of mathematical models in the biosciences. The research featured in this volume began among newly-formed collaborative groups at the 2017 Women Advancing Mathematical Biology Workshop that took place at the Mathematical Biosciences Institute in Columbus, Ohio. The groups spent one intensive week working at MBI and continued their collaborations after the workshop, resulting in the work presented in this volume.

This book describes the evolution of several socio-biological systems using mathematical kinetic theory. Specifically, it deals with modeling and simulations of biological systems whose dynamics follow the rules of mechanics as well as rules governed by their own ability to organize movement and biological functions. It proposes a new biological model focused on the analysis of competition between cells of an aggressive host and cells of a corresponding immune system. Proposed models are related to the generalized Boltzmann equation. The book may be used for advanced graduate courses and seminars in biological systems modeling.

This book describes the evolution of several socio-biological systems using mathematical kinetic theory. Specifically, it deals with modeling and simulations of biological systems whose dynamics follow the rules of mechanics as well as rules governed by their own ability to organize movement and biological functions. It proposes a new biological model focused on the analysis of competition between cells of an aggressive host and cells of a corresponding immune system. Proposed models are related to the generalized Boltzmann equation. The book may be used for advanced graduate courses and seminars in biological systems modeling.

This monograph aims to lay the groundwork for the design of a unified mathematical approach to the modeling and analysis of large, complex systems composed of interacting living things. Drawing on twenty years of research in various scientific fields, it explores how mathematical kinetic theory and evolutionary game theory can be used to understand the complex interplay between mathematical sciences and the dynamics of living systems. The authors hope this will contribute to the development of new tools and strategies, if not a new mathematical theory. The first chapter discusses the main features of living systems and outlines a strategy for their modeling. The following chapters then explore some of the methods needed to potentially achieve this in practice. Chapter Two provides a brief introduction to the mathematical kinetic theory of classical particles, with special emphasis on the Boltzmann equation; the Enskog equation, mean field models, and Monte Carlo methods are also briefly covered. Chapter Three uses concepts from evolutionary game theory to derive mathematical structures that are able to capture the complexity features of interactions within living systems. The book then shifts to exploring the relevant applications of these methods that can potentially be used to derive specific, usable models. The modeling of social systems in various contexts is the subject of Chapter Five, and an overview of modeling crowd dynamics is given in Chapter Six, demonstrating how this approach can be used to model the dynamics of multicellular systems. The final chapter considers some additional applications before presenting an overview of open problems. The authors then offer their own speculations on the conceptual paths that may lead to a mathematical theory of living systems hoping to motivate future research activity in the field. A truly unique contribution to the existing literature, A Quest Toward a Mathematical Theory of Living Systems is an important book that will no doubt have a significant influence on the future directions of the field. It will be of interest to mathematical biologists, systems biologists, biophysicists, and other researchers working on understanding the complexities of living systems.

Mathematics of Bioinformatics: Theory, Methods, and Applications provides a comprehensive format for connecting and integrating information derived from mathematical methods and applying it to the understanding of biological sequences, structures, and networks. Each chapter is divided into a number of sections based on the bioinformatics topics and related mathematical theory and methods. Each topic of the section is comprised of the following three parts: an introduction to the biological problems in bioinformatics; a presentation of relevant topics of mathematical theory and methods to the bioinformatics problems introduced in the first part; an integrative overview that draws the connections and interfaces between bioinformatics problems/issues and mathematical theory/methods/applications.