# differential-equations-models-in-biology-epidemiology-and-ecology

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## Differential Equations Models In Biology Epidemiology And Ecology

**Author :**Stavros Busenberg

**ISBN :**9783642456923

**Genre :**Mathematics

**File Size :**45. 67 MB

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The past forty years have been the stage for the maturation of mathematical biolo~ as a scientific field. The foundations laid by the pioneers of the field during the first half of this century have been combined with advances in ap plied mathematics and the computational sciences to create a vibrant area of scientific research with established research journals, professional societies, deep subspecialty areas, and graduate education programs. Mathematical biology is by its very nature cross-disciplinary, and research papers appear in mathemat ics, biology and other scientific journals, as well as in the specialty journals devoted to mathematical and theoretical biology. Multiple author papers are common, and so are collaborations between individuals who have academic bases in different traditional departments. Those who seek to keep abreast of current trends and problems need to interact with research workers from a much broader spectrum of fields than is common in the traditional mono-culture disciplines. Consequently, it is beneficial to have occasions which bring together significant numbers of workers in this field in a forum that encourages the exchange of ideas and which leads to a timely publication of the work that is presented. Such an occasion occurred during January 13 to 16, 1990 when almost two hun dred research workers participated in an international conference on Differential Equations and Applications to Biology and Population Dynamics which was held in Claremont.

## Differential Equations And Applications To Biology And To Industry Proceedings Of The Claremont International Conference Dedicated To The Memory Of Starvros Busenberg 1941 1993

**Author :**Cooke Kenneth

**ISBN :**9789814549370

**Genre :**

**File Size :**39. 17 MB

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This volume is dedicated to the memory of Professor Stavros Busenberg of Harvey Mudd College, who contributed so greatly to this field during 25 years prior to his untimely death. It contains about 60 invited papers by leading researchers in the areas of dynamical systems, mathematical studies in ecology, epidemics, and physiology, and industrial mathematics. Anyone interested in these areas will find much of value in these contributions.

## Differential Equations Models In Biology Epidemiology And Ecology

**Author :**Stavros Busenberg

**ISBN :**3540542833

**Genre :**Mathematics

**File Size :**85. 62 MB

**Format :**PDF, ePub, Mobi

**Download :**908

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The past forty years have been the stage for the maturation of mathematical biolo~ as a scientific field. The foundations laid by the pioneers of the field during the first half of this century have been combined with advances in ap plied mathematics and the computational sciences to create a vibrant area of scientific research with established research journals, professional societies, deep subspecialty areas, and graduate education programs. Mathematical biology is by its very nature cross-disciplinary, and research papers appear in mathemat ics, biology and other scientific journals, as well as in the specialty journals devoted to mathematical and theoretical biology. Multiple author papers are common, and so are collaborations between individuals who have academic bases in different traditional departments. Those who seek to keep abreast of current trends and problems need to interact with research workers from a much broader spectrum of fields than is common in the traditional mono-culture disciplines. Consequently, it is beneficial to have occasions which bring together significant numbers of workers in this field in a forum that encourages the exchange of ideas and which leads to a timely publication of the work that is presented. Such an occasion occurred during January 13 to 16, 1990 when almost two hun dred research workers participated in an international conference on Differential Equations and Applications to Biology and Population Dynamics which was held in Claremont.

## Mathematics In Population Biology

**Author :**Horst R. Thieme

**ISBN :**9780691187655

**Genre :**Science

**File Size :**23. 58 MB

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## Math And Bio 2010

**Author :**Lynn Arthur Steen

**ISBN :**0883858185

**Genre :**Mathematics

**File Size :**31. 73 MB

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"Math and bio 2010 grew out of 'Meeting the Challenges: Education across the Biological, Mathematical and Computer Sciences,' a joint project of the Mathematical Association of America (MAA), the National Science Foundation Division of Undergraduate Education (NSF DUE), the National Institute of General Medical Sciences (NIGMS), the American Association for the Advancement of Science (AAAS), and the American Society for Microbiology (ASM)."--Foreword, p. vi

## Mathematical Approaches For Emerging And Reemerging Infectious Diseases Models Methods And Theory

**Author :**Carlos Castillo-Chavez

**ISBN :**9781461300656

**Genre :**Medical

**File Size :**56. 68 MB

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This IMA Volume in Mathematics and its Applications MATHEMATICAL APPROACHES FOR EMERGING AND REEMERGING INFECTIOUS DISEASES: MODELS, AND THEORY METHODS is based on the proceedings of a successful one week workshop. The pro ceedings of the two-day tutorial which preceded the workshop "Introduction to Epidemiology and Immunology" appears as IMA Volume 125: Math ematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction. The tutorial and the workshop are integral parts of the September 1998 to June 1999 IMA program on "MATHEMATICS IN BI OLOGY. " I would like to thank Carlos Castillo-Chavez (Director of the Math ematical and Theoretical Biology Institute and a member of the Depart ments of Biometrics, Statistics and Theoretical and Applied Mechanics, Cornell University), Sally M. Blower (Biomathematics, UCLA School of Medicine), Pauline van den Driessche (Mathematics and Statistics, Uni versity of Victoria), and Denise Kirschner (Microbiology and Immunology, University of Michigan Medical School) for their superb roles as organizers of the meetings and editors of the proceedings. Carlos Castillo-Chavez, es pecially, made a major contribution by spearheading the editing process. I am also grateful to Kenneth L. Cooke (Mathematics, Pomona College), for being one of the workshop organizers and to Abdul-Aziz Yakubu (Mathe matics, Howard University) for serving as co-editor of the proceedings. I thank Simon A. Levin (Ecology and Evolutionary Biology, Princeton Uni versity) for providing an introduction.

## Applied Analysis Of Ordinary Differential Equations

**Author :**Sanjeeva Balasuriya

**ISBN :**9783039217267

**Genre :**Science

**File Size :**72. 12 MB

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One might say that ordinary differential equations (notably, in Isaac Newton’s analysis of the motion of celestial bodies) had a central role in the development of modern applied mathematics. This book is devoted to research articles which build upon this spirit: combining analysis with the applications of ordinary differential equations (ODEs). ODEs arise across a spectrum of applications in physics, engineering, geophysics, biology, chemistry, economics, etc., because the rules governing the time-variation of relevant fields is often naturally expressed in terms of relationships between rates of change. ODEs also emerge in stochastic models—for example, when considering the evolution of a probability density function—and in large networks of interconnected agents. The increasing ease of numerically simulating large systems of ODEs has resulted in a plethora of publications in this area; nevertheless, the difficulty of parametrizing models means that the computational results by themselves are sometimes questionable. Therefore, analysis cannot be ignored. This book comprises articles that possess both interesting applications and the mathematical analysis driven by such applications.

## Mathematical Approaches For Emerging And Reemerging Infectious Diseases An Introduction

**Author :**Carlos Castillo-Chavez

**ISBN :**038795354X

**Genre :**Mathematics

**File Size :**32. 91 MB

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This book grew out of the discussions and presentations that began during the Workshop on Emerging and Reemerging Diseases (May 17-21, 1999) sponsored by the Institute for Mathematics and its Application (IMA) at the University of Minnesota with the support of NIH and NSF. The workshop started with a two-day tutorial session directed at ecologists, epidemiologists, immunologists, mathematicians, and scientists interested in the study of disease dynamics. The core of this first volume, Volume 125, covers tutorial and research contributions on the use of dynamical systems (deterministic discrete, delay, PDEs, and ODEs models) and stochastic models in disease dynamics. The volume includes the study of cancer, HIV, pertussis, and tuberculosis. Beginning graduate students in applied mathematics, scientists in the natural, social, or health sciences or mathematicians who want to enter the fields of mathematical and theoretical epidemiology will find this book useful.

## Applications Of Epidemiological Models To Public Health Policymaking

**Author :**Zhilan Feng

**ISBN :**9789814522366

**Genre :**Health & Fitness

**File Size :**30. 99 MB

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Mathematical models can be very helpful to understand the transmission dynamics of infectious diseases. This book presents examples of epidemiological models and modeling tools that can assist policymakers to assess and evaluate disease control strategies. Contents:Mathematical Modeling in Epidemiology:Epidemic ModelsEndemic ModelsApplications to Public Health Policymaking:Applications of Models to Evaluations of Disease Control StrategiesDevelopment of Interactive Tools to Assist Public Health Policymaking Readership: Researchers in mathematical biology, mathematical modeling, infectious diseases and complex systems. Keywords:Epidemiological Model;Population Dynamics;Disease Control StrategyKey Features:Development of modeling tools that are user-friendly to policymakersConsideration of heterogeneities that are not analyzed in detail previouslyConnection of model analyses to real disease data to improve understanding

## Mathematical Understanding Of Infectious Disease Dynamics

**Author :**Stefan Ma

**ISBN :**9789812834836

**Genre :**Mathematics

**File Size :**65. 1 MB

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The Institute for Mathematical Sciences at the National University of Singapore hosted a research program on Mathematical Modeling of Infectious Diseases: Dynamics and Control from 15 August to 9 October 2005. As part of the program, tutorials for graduate students and junior researchers were given by leading experts in the field.

## Ecological Time Series

**Author :**Thomas M. Powell

**ISBN :**9781461517696

**Genre :**Science

**File Size :**32. 97 MB

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This book results from a summer school held at Cornell University in 1992. The participants were graduate students and postdoctoral researchers selected from a broad range of interests and backgrounds in ecological studies. The summer school was the second in a continuing series whose underlying aim and the aim of this volume-is to bring together the different methods and concepts underpinning terrestrial, freshwater, and marine ecology. The first volume in the series focused on patch dynamics in these three ecologi cal sectors. Here we have endeavored to complement that volume by extending its comparative approach to the consideration of ecological time series. The types of data and the methods of collection are necessarily very different in these contrasting environments, yet the underlying concept and the technical problems of analysis have much in common. It proved to be of great interest and value to the summer school participants to see the differences and then work through to an appreciation ofthe generalizable concepts. We believe that such an approach must have value as well for a much larger audience, and we have structured this volume to provide a comparable reading experience.

## Vertically Transmitted Diseases

**Author :**Stavros Busenberg

**ISBN :**9783642753015

**Genre :**Mathematics

**File Size :**65. 73 MB

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Infectious diseases are transmitted through various different mechanisms including person to person interactions, by insect vectors and via vertical transmission from a parent to an unborn offspring. The population dynamics of such disease transmission can be very complicated and the development of rational strategies for controlling and preventing the spread of these diseases requires careful modeling and analysis. The book describes current methods for formulating models and analyzing the dynamics of the propagation of diseases which include vertical transmission as one of the mechanisms for their spread. Generic models that describe broad classes of diseases as well as models that are tailored to the dynamics of a specific infection are formulated and analyzed. The effects of incubation periods, maturation delays, and age-structure, interactions between disease transmission and demographic changes, population crowding, spatial spread, chaotic dynamic behavior, seasonal periodicities and discrete time interval events are studied within the context of specific disease transmission models. No previous background in disease transmission modeling and analysis is assumedand the required biological concepts and mathematical methods are gradually introduced within the context of specific disease transmission models. Graphs are widely used to illustrate and explain the modeling assumptions and results. REMARKS: NOTE: the authors have supplied variants on the promotion text that are more suitable for promotionin different fields (by virtue of different emphasis in the content). They are not enclosed, but in the mathematics editorial.

## Discrete Dynamical Systems And Difference Equations With Mathematica

**Author :**Mustafa R.S. Kulenovic

**ISBN :**9781420035353

**Genre :**Mathematics

**File Size :**60. 72 MB

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Following the work of Yorke and Li in 1975, the theory of discrete dynamical systems and difference equations developed rapidly. The applications of difference equations also grew rapidly, especially with the introduction of graphical-interface software that can plot trajectories, calculate Lyapunov exponents, plot bifurcation diagrams, and find basins of attraction. Modern computer algebra systems have opened the door to the use of symbolic calculation for studying difference equations. This book offers an introduction to discrete dynamical systems and difference equations and presents the Dynamica software. Developed by the authors and based on Mathematica, Dynamica provides an easy-to-use collection of algebraic, numerical, and graphical tools and techniques that allow users to quickly gain the ability to: Find and classify the stability character of equilibrium and periodic points Perform semicycle analysis of solutions Calculate and visualize invariants Calculate and visualize Lyapunov functions and numbers Plot bifurcation diagrams Visualize stable and unstable manifolds Calculate Box Dimension While it presents the essential theoretical concepts and results, the book's emphasis is on using the software. The authors present two sets of Dynamica sessions: one that serves as a tutorial of the different techniques, the other features case studies of well-known difference equations. Dynamica and notebooks corresponding to particular chapters are available for download from the Internet.

## Mathematical Models For Communicable Diseases

**Author :**Fred Brauer

**ISBN :**9781611972412

**Genre :**Mathematics

**File Size :**41. 18 MB

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A self-contained and comprehensive guide to the mathematical modeling of disease transmission, appropriate for graduate students.

## Resource Competition

**Author :**James P. Grover

**ISBN :**9781461563976

**Genre :**Science

**File Size :**76. 52 MB

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As one of the most quantitative of ecological subdisciplines, resource competition is an important, central area of ecology. Recently research into this area has increased dramatically and resource competition models have become more complex. The characterisation of this phenomenon is therefore the aim of this book. Resource Competition seeks to identify the unifying principles emerging from experimental and theoretical approaches as well as the differences between organisms, illustrating that greater knowledge of resource competition will benefit human and environmental welfare. This book will serve as an indispensable guide to ecologists, evolutionary biologists and environmental managers, and all those interested in resource competition as an emerging discipline.

## Advances In Mathematical Population Dynamics Molecules Cells And Man Proceedings Of The 4th International Conference On Mathematical Population Dynamics

**Author :**Arino O

**ISBN :**9789814545976

**Genre :**

**File Size :**21. 22 MB

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This book presents a new approach to the subject of cosmology. It fully exploits Einstein's theory of general relativity. It is found that the most general formal expression of the theory replaces the (10-component) tensor formalism with a (16-component) quaternion formalism. This leads to a unified field theory, where one field incorporates gravitation and electromagnetism. The theory predicts an oscillating universe cosmology with a spiral configuration. Dark matter is explained in terms of a sea of particle-antiparticle pairs, each in a particular (derived) ground state. This leads to an explanation for the separation between matter and antimatter in the universe. There is a brief discussion of black holes and pulsars. The final chapter delves into philosophical considerations such as the different types of ‘truth’, positivism versus realism and a discussion of the role of the Mach principle in physics and cosmology./a

## Mathematical Reviews

**Author :**

**ISBN :**UOM:39015038940535

**Genre :**Mathematics

**File Size :**22. 49 MB

**Format :**PDF, Kindle

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## Frontiers In Mathematical Biology

**Author :**Simon A. Levin

**ISBN :**9783642501241

**Genre :**Mathematics

**File Size :**22. 32 MB

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From a mathematical point of view, physiologically structured population models are an underdeveloped branch of the theory of infinite dimensional dynamical systems. We have called attention to four aspects: (i) A choice has to be made about the kind of equations one extracts from the predominantly verbal arguments about the basic assumptions, and subsequently uses as a starting point for a rigorous mathematical analysis. Though differential equations are easy to formulate (different mechanisms don't interact in infinites imal time intervals and so end up as separate terms in the equations) they may be hard to interpret rigorously as infinitesimal generators. Integral equations constitute an attractive alternative. (ii) The ability of physiologically structured population models to increase our un derstanding of the relation between mechanisms at the i-level and phenomena at the p-level will depend strongly on the development of dynamical systems lab facilities which are applicable to this class of models. (iii) Physiologically structured population models are ideally suited for the for mulation of evolutionary questions. Apart from the special case of age (see Charlesworth 1980, Yodzis 1989, Caswell 1989, and the references given there) hardly any theory exists at the moment. This will, hopefully, change rapidly in the coming years. Again the development of appropriate software may turn out to be crucial.

## Gender Structured Population Modeling

**Author :**M. Iannelli

**ISBN :**9780898715774

**Genre :**Mathematics

**File Size :**26. 25 MB

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This book gives a unified presentation of, and mathematical framework for, modeling population growth by couple formation, summarizing both past and present modeling results. It provides results on model analysis, gives an up-to-date review of mathematical demography, discusses numerical methods, and puts deterministic modeling of human populations into historical perspective.

## Evolution Equations Applications To Physics Industry Life Sciences And Economics

**Author :**Mimmo Iannelli

**ISBN :**9783034880855

**Genre :**Mathematics

**File Size :**45. 62 MB

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The international conference on which the book is based brought together many of the world's leading experts, with particular effort on the interaction between established scientists and emerging young promising researchers, as well as on the interaction of pure and applied mathematics. All material has been rigorously refereed. The contributions contain much material developed after the conference, continuing research and incorporating additional new results and improvements. In addition, some up-to-date surveys are included.