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Mathematical Tools For Understanding Infectious Disease Dynamics

Author : Odo Diekmann
ISBN : 9780691155395
Genre : Mathematics
File Size : 81.27 MB
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Mathematical modeling is critical to our understanding of how infectious diseases spread at the individual and population levels. This book gives readers the necessary skills to correctly formulate and analyze mathematical models in infectious disease epidemiology, and is the first treatment of the subject to integrate deterministic and stochastic models and methods. Mathematical Tools for Understanding Infectious Disease Dynamics fully explains how to translate biological assumptions into mathematics to construct useful and consistent models, and how to use the biological interpretation and mathematical reasoning to analyze these models. It shows how to relate models to data through statistical inference, and how to gain important insights into infectious disease dynamics by translating mathematical results back to biology. This comprehensive and accessible book also features numerous detailed exercises throughout; full elaborations to all exercises are provided. Covers the latest research in mathematical modeling of infectious disease epidemiology Integrates deterministic and stochastic approaches Teaches skills in model construction, analysis, inference, and interpretation Features numerous exercises and their detailed elaborations Motivated by real-world applications throughout
Category: Mathematics

Stochasticity In Processes

Author : Peter Schuster
ISBN : 9783319395029
Genre : Science
File Size : 29.68 MB
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This book has developed over the past fifteen years from a modern course on stochastic chemical kinetics for graduate students in physics, chemistry and biology. The first part presents a systematic collection of the mathematical background material needed to understand probability, statistics, and stochastic processes as a prerequisite for the increasingly challenging practical applications in chemistry and the life sciences examined in the second part. Recent advances in the development of new techniques and in the resolution of conventional experiments at nano-scales have been tremendous: today molecular spectroscopy can provide insights into processes down to scales at which current theories at the interface of physics, chemistry and the life sciences cannot be successful without a firm grasp of randomness and its sources. Routinely measured data is now sufficiently accurate to allow the direct recording of fluctuations. As a result, the sampling of data and the modeling of relevant processes are doomed to produce artifacts in interpretation unless the observer has a solid background in the mathematics of limited reproducibility. The material covered is presented in a modular approach, allowing more advanced sections to be skipped if the reader is primarily interested in applications. At the same time, most derivations of analytical solutions for the selected examples are provided in full length to guide more advanced readers in their attempts to derive solutions on their own. The book employs uniform notation throughout, and a glossary has been added to define the most important notions discussed.
Category: Science

The Basic Approach To Age Structured Population Dynamics

Author : Mimmo Iannelli
ISBN : 9789402411461
Genre : Mathematics
File Size : 53.90 MB
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This book provides an introduction to age-structured population modeling which emphasizes the connection between mathematical theory and underlying biological assumptions. Through the rigorous development of the linear theory and the nonlinear theory alongside numerics, the authors explore classical equations that describe the dynamics of certain ecological systems. Modeling aspects are discussed to show how relevant problems in the fields of demography, ecology and epidemiology can be formulated and treated within the theory. In particular, the book presents extensions of age-structured modeling to the spread of diseases and epidemics while also addressing the issue of regularity of solutions, the asymptotic behavior of solutions, and numerical approximation. With sections on transmission models, non-autonomous models and global dynamics, this book fills a gap in the literature on theoretical population dynamics. The Basic Approach to Age-Structured Population Dynamics will appeal to graduate students and researchers in mathematical biology, epidemiology and demography who are interested in the systematic presentation of relevant models and mathematical methods.
Category: Mathematics

Infectious Disease

Author : Marta Wayne
ISBN : 9780199688937
Genre : Medical
File Size : 32.4 MB
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As doctors and biologists have learned, to their dismay, infectious disease is a moving target: new diseases emerge every year, old diseases evolve into new forms, and ecological and socioeconomic upheavals change the transmission pathways by which disease spread. By taking an approach focused on the general evolutionary and ecological dynamics of disease, this Very Short Introduction provides a general conceptual framework for thinking about disease. Ecology and evolution provide the keys to answering the "where", "why", "how", and "what" questions about any particular infectious disease: where did it come from? How is it transmitted from one person to another, and why are some individuals more susceptible than others? What biochemical, ecological, and evolutionary strategies can be used to combat the disease? Is it more effective to block transmission at the population level, or to block infection at the individual level? Through a series of case studies, Benjamin Bolker and Marta L. Wayne introduce the major ideas of infectious disease in a clear and thoughtful way, emphasizing the general principles of infection, the management of outbreaks, and the evolutionary and ecological approaches that are now central to much research about infectious disease. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Category: Medical

Individual Based Modeling And Ecology

Author : Volker Grimm
ISBN : 069109666X
Genre : Computers
File Size : 57.83 MB
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Individual-based models are an exciting and widely used new tool for ecology. These computational models allow scientists to explore the mechanisms through which population and ecosystem ecology arises from how individuals interact with each other and their environment. This book provides the first in-depth treatment of individual-based modeling and its use to develop theoretical understanding of how ecological systems work, an approach the authors call "individual-based ecology." Grimm and Railsback start with a general primer on modeling: how to design models that are as simple as possible while still allowing specific problems to be solved, and how to move efficiently through a cycle of pattern-oriented model design, implementation, and analysis. Next, they address the problems of theory and conceptual framework for individual-based ecology: What is "theory"? That is, how do we develop reusable models of how system dynamics arise from characteristics of individuals? What conceptual framework do we use when the classical differential equation framework no longer applies? An extensive review illustrates the ecological problems that have been addressed with individual-based models. The authors then identify how the mechanics of building and using individual-based models differ from those of traditional science, and provide guidance on formulating, programming, and analyzing models. This book will be helpful to ecologists interested in modeling, and to other scientists interested in agent-based modeling.
Category: Computers

Philosophical Transactions Of The Royal Society Of London

Author :
ISBN : CORNELL:31924090179403
Genre : AIDS (Disease)
File Size : 26.78 MB
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Each issue of Transactions B is devoted to a specific area of the biological sciences, including clinical science. All papers are peer reviewed and edited to the highest standards. Published on the 29th of each month, Transactions B is essential reading for all biologists.
Category: AIDS (Disease)

Evolutionary Dynamics

Author : Martin A. Nowak
ISBN : 9780674417748
Genre : Science
File Size : 61.68 MB
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At a time of unprecedented expansion in the life sciences, evolution is the one theory that transcends all of biology. Any observation of a living system must ultimately be interpreted in the context of its evolution. Evolutionary change is the consequence of mutation and natural selection, which are two concepts that can be described by mathematical equations. Evolutionary Dynamics is concerned with these equations of life. In this book, Martin A. Nowak draws on the languages of biology and mathematics to outline the mathematical principles according to which life evolves. His work introduces readers to the powerful yet simple laws that govern the evolution of living systems, no matter how complicated they might seem. Evolution has become a mathematical theory, Nowak suggests, and any idea of an evolutionary process or mechanism should be studied in the context of the mathematical equations of evolutionary dynamics. His book presents a range of analytical tools that can be used to this end: fitness landscapes, mutation matrices, genomic sequence space, random drift, quasispecies, replicators, the Prisoner’s Dilemma, games in finite and infinite populations, evolutionary graph theory, games on grids, evolutionary kaleidoscopes, fractals, and spatial chaos. Nowak then shows how evolutionary dynamics applies to critical real-world problems, including the progression of viral diseases such as AIDS, the virulence of infectious agents, the unpredictable mutations that lead to cancer, the evolution of altruism, and even the evolution of human language. His book makes a clear and compelling case for understanding every living system—and everything that arises as a consequence of living systems—in terms of evolutionary dynamics.
Category: Science

Books In Print

Author :
ISBN : STANFORD:36105015915866
Genre : American literature
File Size : 30.29 MB
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Category: American literature