Mathematics and Life Sciences

Alexandra V. Antoniouk, Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine; Roderick V. N. Melnik, Wilfrid Laurier University, Waterloo, Ontario, Canada.

The book provides a unique collection of in-depth mathematical, statistical, and modeling methods and techniques for life sciences, as well as their applications in a number of areas within life sciences. The book provides also with a range of new ideas that represent emerging frontiers in life sciences where the application of such quantitative methods and techniques is becoming increasingly important.

Many areas within life sciences are becoming increasingly quantitative and the progress in those areas will be more and more dependent on the successful development of advanced mathematical, statistical and modelling methodologies and techniques. The state-of-the-art developments in such methodologies and techniques are scattered throughout research journals and hardly accessible to the practitioners in those areas. This book identifies a number of frontier areas where such methodologies and techniques have recently been developed and are to be published here for the first time, bringing substantial potential benefit to a range of applications in life sciences. In addition, the book contains several state-of-the-art surveys at the interface of mathematics and life sciences that would benefit a larger interdisciplinary community.

It is aimed at researchers in academia, practitioners and graduate students who want to foster interdisciplinary collaborations required to meet the challenges at the interface of modern life sciences and mathematics.

The De Gruyter Series in Mathematics and Life Sciences is devoted to the publication of monographs in the field. They cover topics and methods in fields of current interest that use mathematical approaches to understand and explain, model and influence phenomena in all areas of life sciences. This includes, among others, theory and application of biological mathematical modeling, complex systems biology, bioinformatics, computational biomodeling stochastic modeling, biostatistics, computational evolutionary biology, comparative genomics, or structural bioinformatics. Also, new types of mathematical problems that arise from biological knowledge shall be covered.

The book contains 12 state-of-the-art surveys and research articles at the interface of mathematics and life sciences. In particular it focuses on the following areas grouped in chapters:

• Ensemble Modeling of Biological Systems;
• Nonlinear Levy and Feller Processes and Their Applications;
• New Mathematical Results on Epidemic Models;
• Mathematical Analysis of PDE-based Models in Cell Biology;
• Axiomatic Modeling in Life Sciences;
• Theory and Applications of Nonlinear PDEs in Life Sciences;
• Pattern Formation Models with Applications in Developmental Biology;
• Modeling the Dynamics of Genetic Mechanisms;
• Statistical Modeling in Radiation Medicine;
• Physiological Effects of Physical Fields, Biological Response and Acute Pain Models;
• Approaches to Modelling Avascular Tumour Growth.

The Introductory part provides a description of the current challenges at the interface of mathematics and life sciences and a summary of the main topics covered by this book.