Mathematics and Life Sciences
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Edited by:
Alexandra V. Antoniouk
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With contributions by:
Robert Anderssen
About this book
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.
Author / Editor information
Alexandra V. Antoniouk, Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine; Roderick V. N. Melnik, Wilfrid Laurier University, Waterloo, Ontario, Canada.
Supplementary Materials
Topics
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Frontmatter
i -
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Preface
vii -
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Contents
ix - 1 Introduction
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1.1 Scientific Frontiers at the Interface of Mathematics and Life Sciences
3 - 2 Mathematical and Statistical Modeling of Biological Systems
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2.1 Ensemble Modeling of Biological Systems
19 - 3 Probabilistic Models for Nonlinear Processes and Biological Dynamics
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3.1 Nonlinear Lévy and Nonlinear Feller Processes: an Analytic Introduction
45 - 4 New Results in Mathematical Epidemiology and Modeling Dynamics of Infectious Diseases
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4.1 Formal Solutions of Epidemic Equation
73 - 5 Mathematical Analysis of PDE-based Models and Applications in Cell Biology
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5.1 Asymptotic Analysis of the Dirichlet Spectral Problems in Thin Perforated Domains with Rapidly Varying Thickness and Different Limit Dimensions
89 - 6 Axiomatic Modeling in Life Sciences with Case Studies for Virus-immune System and Oncolytic Virus Dynamics
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6.1 AxiomaticModeling in Life Sciences
113 - 7 Theory, Applications, and Control of Nonlinear PDEs in Life Sciences
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7.1 On One Semilinear Parabolic Equation of Normal Type
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7.2 On some Classes of Nonlinear Equations with L1-Data
161 - 8 Mathematical Models of Pattern Formation and Their Applications in Developmental Biology
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8.1 Reaction-Diffusion Models of Pattern Formation in Developmental Biology
191 - 9 Modeling the Dynamics of Genetic Mechanism, Pattern Formation, and the Genetics of “Geometry”
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9.1 Modeling the Positioning of Trichomes on the Leaves of Plants
215 - 10 Statistical Modeling in Life Sciences and Direct Measurements
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10.1 Error Estimation for Direct Measurements in May–June 1986 of 131I Radioactivity in Thyroid Gland of Children and Adolescents and Their Registration in Risk Analysis
231 - 11 Design and Development of Experiments for Life Science Applications
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11.1 Physiological Effects of Static Magnetic Field Exposure in an in vivo Acute Visceral Pain Model in Mice
247 - 12 Mathematical Biomedicine and Modeling Avascular Tumor Growth
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12.1 Continuum Models of Avascular Tumor Growth
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Index
313
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