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Dynamical Systems for Biological Modeling

Dynamical Systems for Biological Modeling
Author: Fred Brauer
Publisher: CRC Press
Total Pages: 482
Release: 2015-12-23
Genre: Mathematics
ISBN: 1498774040

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Dynamical Systems for Biological Modeling: An Introduction prepares both biology and mathematics students with the understanding and techniques necessary to undertake basic modeling of biological systems. It achieves this through the development and analysis of dynamical systems.The approach emphasizes qualitative ideas rather than explicit computa


Modeling Dynamic Biological Systems

Modeling Dynamic Biological Systems
Author: Bruce Hannon
Publisher: Springer Science & Business Media
Total Pages: 399
Release: 2012-12-06
Genre: Science
ISBN: 1461206510

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Models help us understand the dynamics of real-world processes by using the computer to mimic the actual forces that are known or assumed to result in a system's behavior. This book does not require a substantial background in mathematics or computer science.


Applications of Dynamical Systems in Biology and Medicine

Applications of Dynamical Systems in Biology and Medicine
Author: Trachette Jackson
Publisher: Springer
Total Pages: 240
Release: 2015-07-06
Genre: Mathematics
ISBN: 1493927825

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This volume highlights problems from a range of biological and medical applications that can be interpreted as questions about system behavior or control. Topics include drug resistance in cancer and malaria, biological fluid dynamics, auto-regulation in the kidney, anti-coagulation therapy, evolutionary diversification and photo-transduction. Mathematical techniques used to describe and investigate these biological and medical problems include ordinary, partial and stochastic differentiation equations, hybrid discrete-continuous approaches, as well as 2 and 3D numerical simulation.


Modeling Life

Modeling Life
Author: Alan Garfinkel
Publisher: Springer
Total Pages: 456
Release: 2017-09-06
Genre: Mathematics
ISBN: 3319597310

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This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?


The Dynamics of Biological Systems

The Dynamics of Biological Systems
Author: Arianna Bianchi
Publisher: Springer Nature
Total Pages: 267
Release: 2019-10-02
Genre: Mathematics
ISBN: 3030225836

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The book presents nine mini-courses from a summer school, Dynamics of Biological Systems, held at the University of Alberta in 2016, as part of the prestigious seminar series: Séminaire de Mathématiques Supérieures (SMS). It includes new and significant contributions in the field of Dynamical Systems and their applications in Biology, Ecology, and Medicine. The chapters of this book cover a wide range of mathematical methods and biological applications. They - explain the process of mathematical modelling of biological systems with many examples, - introduce advanced methods from dynamical systems theory, - present many examples of the use of mathematical modelling to gain biological insight - discuss innovative methods for the analysis of biological processes, - contain extensive lists of references, which allow interested readers to continue the research on their own. Integrating the theory of dynamical systems with biological modelling, the book will appeal to researchers and graduate students in Applied Mathematics and Life Sciences.


Dynamic Models in Biology

Dynamic Models in Biology
Author: Stephen P. Ellner
Publisher: Princeton University Press
Total Pages: 352
Release: 2011-09-19
Genre: Science
ISBN: 1400840961

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From controlling disease outbreaks to predicting heart attacks, dynamic models are increasingly crucial for understanding biological processes. Many universities are starting undergraduate programs in computational biology to introduce students to this rapidly growing field. In Dynamic Models in Biology, the first text on dynamic models specifically written for undergraduate students in the biological sciences, ecologist Stephen Ellner and mathematician John Guckenheimer teach students how to understand, build, and use dynamic models in biology. Developed from a course taught by Ellner and Guckenheimer at Cornell University, the book is organized around biological applications, with mathematics and computing developed through case studies at the molecular, cellular, and population levels. The authors cover both simple analytic models--the sort usually found in mathematical biology texts--and the complex computational models now used by both biologists and mathematicians. Linked to a Web site with computer-lab materials and exercises, Dynamic Models in Biology is a major new introduction to dynamic models for students in the biological sciences, mathematics, and engineering.


Modeling Methods for Medical Systems Biology

Modeling Methods for Medical Systems Biology
Author: María Elena Álvarez-Buylla Roces
Publisher: Springer
Total Pages: 258
Release: 2018-08-03
Genre: Science
ISBN: 3319893548

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This book contributes to better understand how lifestyle modulations can effectively halt the emergence and progression of human diseases. The book will allow the reader to gain a better understanding of the mechanisms by which the environment interferes with the bio-molecular regulatory processes underlying the emergence and progression of complex diseases, such as cancer. Focusing on key and early cellular bio-molecular events giving rise to the emergence of degenerative chronic disease, it builds on previous experience on the development of multi-cellular organisms, to propose a mathematical and computer based framework that allows the reader to analyze the complex interplay between bio-molecular processes and the (micro)-environment from an integrative, mechanistic, quantitative and dynamical perspective. Taking the wealth of empirical evidence that exists it will show how to build and analyze models of core regulatory networks involved in the emergence and progression of chronic degenerative diseases, using a bottom-up approach.


Dynamic Systems Biology Modeling and Simulation

Dynamic Systems Biology Modeling and Simulation
Author: Joseph DiStefano III
Publisher: Academic Press
Total Pages: 886
Release: 2015-01-10
Genre: Science
ISBN: 0124104932

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Dynamic Systems Biology Modeling and Simuation consolidates and unifies classical and contemporary multiscale methodologies for mathematical modeling and computer simulation of dynamic biological systems – from molecular/cellular, organ-system, on up to population levels. The book pedagogy is developed as a well-annotated, systematic tutorial – with clearly spelled-out and unified nomenclature – derived from the author’s own modeling efforts, publications and teaching over half a century. Ambiguities in some concepts and tools are clarified and others are rendered more accessible and practical. The latter include novel qualitative theory and methodologies for recognizing dynamical signatures in data using structural (multicompartmental and network) models and graph theory; and analyzing structural and measurement (data) models for quantification feasibility. The level is basic-to-intermediate, with much emphasis on biomodeling from real biodata, for use in real applications. Introductory coverage of core mathematical concepts such as linear and nonlinear differential and difference equations, Laplace transforms, linear algebra, probability, statistics and stochastics topics The pertinent biology, biochemistry, biophysics or pharmacology for modeling are provided, to support understanding the amalgam of “math modeling” with life sciences Strong emphasis on quantifying as well as building and analyzing biomodels: includes methodology and computational tools for parameter identifiability and sensitivity analysis; parameter estimation from real data; model distinguishability and simplification; and practical bioexperiment design and optimization Companion website provides solutions and program code for examples and exercises using Matlab, Simulink, VisSim, SimBiology, SAAMII, AMIGO, Copasi and SBML-coded models A full set of PowerPoint slides are available from the author for teaching from his textbook. He uses them to teach a 10 week quarter upper division course at UCLA, which meets twice a week, so there are 20 lectures. They can easily be augmented or stretched for a 15 week semester course Importantly, the slides are editable, so they can be readily adapted to a lecturer’s personal style and course content needs. The lectures are based on excerpts from 12 of the first 13 chapters of DSBMS. They are designed to highlight the key course material, as a study guide and structure for students following the full text content The complete PowerPoint slide package (~25 MB) can be obtained by instructors (or prospective instructors) by emailing the author directly, at: [email protected]


An Introduction to Dynamical Systems for Biological Modeling

An Introduction to Dynamical Systems for Biological Modeling
Author: Fred Brauer
Publisher: Chapman & Hall/CRC
Total Pages:
Release: 2014-10
Genre: Biology
ISBN: 9781466599857

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Taking more of a qualitative rather than computational approach, this text presents the techniques required to undertake basic modelling of biological systems through the development and analysis of dynamical systems. It includes many different types of applications from population biology and epidemiology.


Biological Modeling and Simulation

Biological Modeling and Simulation
Author: Russell Schwartz
Publisher: MIT Press
Total Pages: 403
Release: 2008-07-25
Genre: Science
ISBN: 0262303396

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A practice-oriented survey of techniques for computational modeling and simulation suitable for a broad range of biological problems. There are many excellent computational biology resources now available for learning about methods that have been developed to address specific biological systems, but comparatively little attention has been paid to training aspiring computational biologists to handle new and unanticipated problems. This text is intended to fill that gap by teaching students how to reason about developing formal mathematical models of biological systems that are amenable to computational analysis. It collects in one place a selection of broadly useful models, algorithms, and theoretical analysis tools normally found scattered among many other disciplines. It thereby gives the aspiring student a bag of tricks that will serve him or her well in modeling problems drawn from numerous subfields of biology. These techniques are taught from the perspective of what the practitioner needs to know to use them effectively, supplemented with references for further reading on more advanced use of each method covered. The text, which grew out of a class taught at Carnegie Mellon University, covers models for optimization, simulation and sampling, and parameter tuning. These topics provide a general framework for learning how to formulate mathematical models of biological systems, what techniques are available to work with these models, and how to fit the models to particular systems. Their application is illustrated by many examples drawn from a variety of biological disciplines and several extended case studies that show how the methods described have been applied to real problems in biology.