Advanced Topics In Biomathematics

This book provides an excellent overview of current developments in a wide range of topics in biomathematics, such as population dynamics, neural networks, fishery markets, transmission of infectious diseases, genetic analysis, biostatistics and biomechanics. The contributors are leading researchers from Australia, Canada, the People's Republic of China, Hungary, Iceland, Italy, Japan, Singapore and the USA.

This book provides an excellent overview of current developments in a wide range of topics in biomathematics, such as population dynamics, neural networks, fishery markets, transmission of infectious diseases, genetic analysis, biostatistics and biomechanics. The contributors are leading researchers from Australia, Canada, the People's Republic of China, Hungary, Iceland, Italy, Japan, Singapore and the USA.

This book analyzes the impact of quiescent phases on biological models. Quiescence arises, for example, when moving individuals stop moving, hunting predators take a rest, infected individuals are isolated, or cells enter the quiescent compartment of the cell cycle. In the first chapter of Topics in Mathematical Biology general principles about coupled and quiescent systems are derived, including results on shrinking periodic orbits and stabilization of oscillations via quiescence. In subsequent chapters classical biological models are presented in detail and challenged by the introduction of quiescence. These models include delay equations, demographic models, age structured models, Lotka-Volterra systems, replicator systems, genetic models, game theory, Nash equilibria, evolutionary stable strategies, ecological models, epidemiological models, random walks and reaction-diffusion models. In each case we find new and interesting results such as stability of fixed points and/or periodic orbits, excitability of steady states, epidemic outbreaks, survival of the fittest, and speeds of invading fronts. The textbook is intended for graduate students and researchers in mathematical biology who have a solid background in linear algebra, differential equations and dynamical systems. Readers can find gems of unexpected beauty within these pages, and those who knew K.P. (as he was often called) well will likely feel his presence and hear him speaking to them as they read.

This book is based on a one semester course that the authors have been teaching for several years, and includes two sets of case studies. The first includes chemostat models, predator-prey interaction, competition among species, the spread of infectious diseases, and oscillations arising from bifurcations. In developing these topics, readers will also be introduced to the basic theory of ordinary differential equations, and how to work with MATLAB without having any prior programming experience. The second set of case studies were adapted from recent and current research papers to the level of the students. Topics have been selected based on public health interest. This includes the risk of atherosclerosis associated with high cholesterol levels, cancer and immune interactions, cancer therapy, and tuberculosis. Readers will experience how mathematical models and their numerical simulations can provide explanations that guide biological and biomedical research. Considered to be the undergraduate companion to the more advanced book "Mathematical Modeling of Biological Processes" (A. Friedman, C.-Y. Kao, Springer – 2014), this book is geared towards undergraduate students with little background in mathematics and no biological background.

Featuring contributions from experts in mathematical biology and biomedical research, this edited volume covers a diverse set of topics on mathematical methods and applications in the biosciences. Topics focus on advanced mathematical methods, with chapters on the mathematical analysis of the quasispecies model, Arnold’s weak resonance equation, bifurcation analysis, and the Tonnelier-Gerstner model. Special emphasis is placed on applications such as natural selection, population heterogeneity, polyvariant ontogeny in plants, cancer dynamics, and analytical solutions for traveling pulses and wave trains in neural models. A survey on quasiperiodic topology is also presented in this book. Carefully peer-reviewed, this volume is suitable for students interested in interdisciplinary research. Researchers in applied mathematics and the biosciences will find this book an important resource on the latest developments in the field. In keeping with the STEAM-H series, the editors hope to inspire interdisciplinary understanding and collaboration.

Genome-wide association studies (GWAS) have been widely used in the genetic dissection of complex traits. However, there are still limits in current GWAS statistics. For example, (1) almost all the existing methods do not estimate additive and dominance effects in quantitative trait nucleotide (QTN) detection; (2) the methods for detecting QTN-by-environment interaction (QEI) are not straightforward and do not estimate additive and dominance effects as well as additive-by-environment and dominance-by-environment interaction effects, leading to unreliable results; and (3) no or too simple polygenic background controls have been employed in QTN-by-QTN interaction (QQI) detection. As a result, few studies of QEI and QQI for complex traits have been reported based on multiple-environment experiments. Recently, new statistical tools, including 3VmrMLM, have been developed to address these needs in GWAS. In 3VmrMLM, all the trait-associated effects, including QTN, QEI and QQI related effects, are compressed into a single effect-related vector, while all the polygenic backgrounds are compressed into a single polygenic effect matrix. These compressed parameters can be accurately and efficiently estimated through a unified mixed model analysis. To further validate these new GWAS methods, particularly 3VmrMLM, they should be rigorously tested in real data of various plants and a wide range of other species.

Speaking directly to the growing importance of research experience in undergraduate mathematics programs, this volume offers suggestions for undergraduate-appropriate research projects in mathematical and computational biology for students and their faculty mentors. The aim of each chapter is twofold: for faculty, to alleviate the challenges of identifying accessible topics and advising students through the research process; for students, to provide sufficient background, additional references, and context to excite students in these areas and to enable them to successfully undertake these problems in their research. Some of the topics discussed include: • Oscillatory behaviors present in real-world applications, from seasonal outbreaks of childhood diseases to action potentials in neurons • Simulating bacterial growth, competition, and resistance with agent-based models and laboratory experiments • Network structure and the dynamics of biological systems • Using neural networks to identify bird species from birdsong samples • Modeling fluid flow induced by the motion of pulmonary cilia Aimed at undergraduate mathematics faculty and advanced undergraduate students, this unique guide will be a valuable resource for generating fruitful research collaborations between students and faculty.