Applying mathematics to biology has a long history, but only recently has there been an explosion of interest in the field. Some reasons for this include: the explosion of data-rich information sets, due to the genomics revolution, which are difficult to understand without the use of analytical tools, recent development of mathematical tools such as chaos theory to help understand complex, non-linear mechanisms in biology, an increase in computing power which enables calculations and simulations to be performed that were not previously possible, and an increasing interest in in-silico experimentation due to the complications involved in human and animal research. This new book presents the latest leading-edge research in the field.

This is the only book that teaches all aspects of modern mathematical modeling and that is specifically designed to introduce undergraduate students to problem solving in the context of biology. Included is an integrated package of theoretical modeling and analysis tools, computational modeling techniques, and parameter estimation and model validation methods, with a focus on integrating analytical and computational tools in the modeling of biological processes. Divided into three parts, it covers basic analytical modeling techniques; introduces computational tools used in the modeling of biological problems; and includes various problems from epidemiology, ecology, and physiology. All chapters include realistic biological examples, including many exercises related to biological questions. In addition, 25 open-ended research projects are provided, suitable for students. An accompanying Web site contains solutions and a tutorial for the implementation of the computational modeling techniques. Calculations can be done in modern computing languages such as Maple, Mathematica, and MATLAB?.

A one-of-a-kind guide to using deterministic and probabilistic methods for solving problems in the biological sciences Highlighting the growing relevance of quantitative techniques in scientific research, Mathematical Methods in Biology provides an accessible presentation of the broad range of important mathematical methods for solving problems in the biological sciences. The book reveals the growing connections between mathematics and biology through clear explanations and specific, interesting problems from areas such as population dynamics, foraging theory, and life history theory. The authors begin with an introduction and review of mathematical tools that are employed in subsequent chapters, including biological modeling, calculus, differential equations, dimensionless variables, and descriptive statistics. The following chapters examine standard discrete and continuous models using matrix algebra as well as difference and differential equations. Finally, the book outlines probability, statistics, and stochastic methods as well as material on bootstrapping and stochastic differential equations, which is a unique approach that is not offered in other literature on the topic. In order to demonstrate the application of mathematical methods to the biological sciences, the authors provide focused examples from the field of theoretical ecology, which serve as an accessible context for study while also demonstrating mathematical skills that are applicable to many other areas in the life sciences. The book's algorithms are illustrated using MATLAB®, but can also be replicated using other software packages, including R, Mathematica®, and Maple; however, the text does not require any single computer algebra package. Each chapter contains numerous exercises and problems that range in difficulty, from the basic to more challenging, to assist readers with building their problem-solving skills. Selected solutions are included at the back of the book, and a related Web site features supplemental material for further study. Extensively class-tested to ensure an easy-to-follow format, Mathematical Methods in Biology is an excellent book for mathematics and biology courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for researchers and professionals working in the fields of biology, ecology, and biomathematics.

With the spread of COVID-19, Mathematical Biology has gained significant prominence not just among the scientific community but also population-wide. This volume is a collection of state-of-the-art research on this subject. Infectious diseases are highlighted in this volume with novel results on the Zika-dengue interactions, malaria-HIV interactions, and cholera, which in the last decade were the causes of problems in public health.Readers will find chapters that address novel mathematical techniques for studying infectious disease models, such as methods for deriving the basic reproduction numbers in reaction-diffusion epidemic models, and methods for studying epidemic models on networks. Several chapters are focused on population dynamics and ecological interactions. Here novel techniques for approximation of stochastic population processes have been developed and types of predator-prey models have been established and investigated.Cancer is one of the non-infectious killer diseases of the 21st century. The chapters here study angiogenesis and angio-genesis therapy and apply optimal control to the tumor-immune interaction model.

This volume is a collection of papers on various areas of current interest in mathematical biology, such as epidemic disease modeling, including the effects of vaccination and strain replacement; immunology, such as T-Cell dynamics and the mechanism of phagocytosis; knot theory; DNA computation; and Boolean networks.

Featuring research from the 2017 research symposium of the Association for Women in Mathematics, this volume presents recent findings in pure mathematics and a range of advances and novel applications in fields such as engineering, biology, and medicine. Featured topics include geometric group theory, generalized iterated wreath products of cyclic groups and symmetric groups, Conway-Coxeter friezes and mutation, and classroom experiments in teaching collegiate mathematics. A review of DNA topology and a computational study of learning-induced sequence reactivation during sharp-wave ripples are also included in this volume. Numerous illustrations and tables convey key results throughout the book. This volume highlights research from women working in academia, industry, and government. It is a helpful resource for researchers and graduate students interested in an overview of the latest research in mathematics.

Progress in plant biology relies on the quantification, analysis and mathematical modeling of data over different time and length scales. This book describes common mathematical and computational approaches as well as some carefully chosen case studies that demonstrate the use of these techniques to solve problems at the forefront of plant biology. Each chapter is written by an expert in field with the goal of conveying concepts whilst at the same time providing sufficient background and links to available software for readers to rapidly build their own models and run their own simulations. This book is aimed at postgraduate students and researchers working the field of plant systems biology and synthetic biology, but will also be a useful reference for anyone wanting to get into quantitative plant biology.