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Mathematical modeling can be a useful tool for researchers in the biological scientists. Yet in biological modeling there is no one modeling technique that is suitable for all problems. Instead, different problems call for different approaches. Furthermore, it can be helpful to analyze the same system using a variety of approaches, to be able to exploit the advantages and drawbacks of each. In practice, it is often unclear which modeling approaches will be most suitable for a particular biological question, a problem which requires researchers to know a reasonable amount about a number of techniques, rather than become experts on a single one. "Introduction to Modeling for Biosciences" addresses this issue by presenting a broad overview of the most important techniques used to model biological systems. In addition to providing an introduction into the use of a wide range of software tools and modeling environments, this helpful text/reference describes the constraints and difficulties that each modeling technique presents in practice, enabling the researcher to quickly determine which software package would be most useful for their particular problem. Topics and features: introduces a basic array of techniques to formulate models of biological systems, and to solve them; intersperses the text with exercises throughout the book; includes practical introductions to the Maxima computer algebra system, the PRISM model checker, and the Repast Simphony agent modeling environment; discusses agent-based models, stochastic modeling techniques, differential equations and Gillespie’s stochastic simulation algorithm; contains appendices on Repast batch running, rules of differentiation and integration, Maxima and PRISM notation, and some additional mathematical concepts; supplies source code for many of the example models discussed, at the associated website http://www.cs.kent.ac.uk/imb/. This unique and practical guide leads the novice modeler through realistic and concrete modeling projects, highlighting and commenting on the process of abstracting the real system into a model. Students and active researchers in the biosciences will also benefit from the discussions of the high-quality, tried-and-tested modeling tools described in the book. Dr. David J. Barnes is a lecturer in computer science at the University of Kent, UK, with a strong background in the teaching of programming. Dr. Dominique Chu is a lecturer in computer science at the University of Kent, UK. He is an internationally recognized expert in agent-based modeling, and has also in-depth research experience in stochastic and differential equation based modeling.
This accessible text presents a detailed introduction to the use of a wide range of software tools and modeling environments for use in the biosciences, as well as the fundamental mathematical background. The practical constraints presented by each modeling technique are described in detail, enabling the researcher to determine which software package would be most useful for a particular problem. Features: introduces a basic array of techniques to formulate models of biological systems, and to solve them; discusses agent-based models, stochastic modeling techniques, differential equations, spatial simulations, and Gillespie’s stochastic simulation algorithm; provides exercises; describes such useful tools as the Maxima algebra system, the PRISM model checker, and the modeling environments Repast Simphony and Smoldyn; contains appendices on rules of differentiation and integration, Maxima and PRISM notation, and some additional mathematical concepts; offers supplementary material at an associated website.
Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation. Notes on some mathematical background (calculus, matrix algebra, differential equations, and probability) have been prepared and may be downloaded at the web site of the Centre for Disease Modeling (www.cdm.yorku.ca).
This comprehensive textbook/reference provides an in-depth overview of the key aspects of transportation analysis, with an emphasis on modeling real transportation systems and executing the models. Topics and features: presents comprehensive review questions at the end of each chapter, together with detailed case studies, useful links, references and suggestions for further reading; supplies a variety of teaching support materials at the book’s webpage on Springer.com, including a complete set of lecture slides; examines the classification of models used for multimodal transportation systems, and reviews the models and evaluation methods used in transportation planning; explains traffic assignment to road networks, and describes computer simulation integration platforms and their use in the transportation systems sector; provides an overview of transportation simulation tools, and discusses the critical issues in the design, development and use of the simulation models.
This book illustrates how models of complex systems are built up and provides indispensable mathematical tools for studying their dynamics. This second edition includes more recent research results and many new and improved worked out examples and exercises.
The challenge for the biosciences in the twenty-first century is to integrate genome sequencing information into a better understanding of biology, physiology, and human pathology. Such attempts at integration are moving the world toward a new generation of bioscience and bioengineering, where biological, physiological, and pathological information from humans and other living animals can be quantitatively described in silico across multiple scales of time and size and through diverse hierarchies of organization — from molecules to cells and organs, to individuals. To "harness" such complexity, international communities of integrative bioscientists and bioengineers aim to establish frameworks and information infrastructures for describing biological structures and physiological functions on multiple scales of time and space. This textbook includes a public platform to describe physiological functions using mathematical equations and guides the reader to perform mathematical modeling and computer simulations, to combine existing models as well as to create new models. Accessible to biologists, physiologists, and students of the sciences, with illustrative details provided when necessary, this book seeks to achieve a systematic way of harnessing biological complexity. Sharing the databases among communities worldwide will help to find comprehensive answers to all the important questions.
This book presents a series of models in the general area of cell physiology and signal transduction, with particular attention being paid to intracellular calcium dynamics, and the role played by calcium in a variety of cell types. Calcium plays a crucial role in cell physiology, and the study of its dynamics lends insight into many different cellular processes. In particular, calcium plays a central role in muscular contraction, olfactory transduction and synaptic communication, three of the topics to be addressed in detail in this book. In addition to the models, much of the underlying physiology is presented, so that readers may learn both the mathematics and the physiology, and see how the models are applied to specific biological questions. It is intended primarily as a graduate text or a research reference. It will serve as a concise and up-to-date introduction to all those who wish to learn about the state of calcium dynamics modeling, and how such models are applied to physiological questions.

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