Mathematical Models for Spatial Heterogeneity in Population Dynamics and Epidemiology PDF Download
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Author: Alun Lewis Lloyd
Publisher:
ISBN:
Category : Animal populations
Languages : en
Pages : 175
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Book Description
Author: Alun Lewis Lloyd
Publisher:
ISBN:
Category : Animal populations
Languages : en
Pages : 175
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Book Description
Author: Fred Brauer
Publisher: Springer Science & Business Media
ISBN: 1475735162
Category : Science
Languages : en
Pages : 432
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Book Description
The goal of this book is to search for a balance between simple and analyzable models and unsolvable models which are capable of addressing important questions on population biology. Part I focusses on single species simple models including those which have been used to predict the growth of human and animal population in the past. Single population models are, in some sense, the building blocks of more realistic models -- the subject of Part II. Their role is fundamental to the study of ecological and demographic processes including the role of population structure and spatial heterogeneity -- the subject of Part III. This book, which will include both examples and exercises, is of use to practitioners, graduate students, and scientists working in the field.
Author: Fred Brauer
Publisher: Springer
ISBN: 9781461416876
Category : Mathematics
Languages : en
Pages : 508
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Book Description
The goal of this book is to search for a balance between simple and analyzable models and unsolvable models which are capable of addressing important questions on population biology. Part I focusses on single species simple models including those which have been used to predict the growth of human and animal population in the past. Single population models are, in some sense, the building blocks of more realistic models -- the subject of Part II. Their role is fundamental to the study of ecological and demographic processes including the role of population structure and spatial heterogeneity -- the subject of Part III. This book, which will include both examples and exercises, is of use to practitioners, graduate students, and scientists working in the field.
Author: Tianren Zhai
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Mathematical models provide powerful tools to explain and predict population dynamics. A central problem is to study the long-term behavior of modeling systems. The patch models and reaction-diffusion models are widely applied to describe spatial heterogeneity and habitat connectivity. Basic reproduction number R0 plays an important role in mathematical biology. In epidemiology, R0 stands for the expected number of secondary cases produced in a completely susceptible population by a typical infective individual. The value of R0 can determines the persistence or extinction of population. Nowadays, characterizing the basic reproduction number due to the effects of parameters becomes very significant for predicting and controlling disease transmission. This thesis consists of three chapters. In Chapter 1, we investigate the effect of spatial heterogeneity on the basic reproduction number for an SIS epidemic patch model, and compute R0 numerically to show the influence of the spatial heterogeneity and movement. Chapter 2 is devoted to the study of the global dynamics of a reaction diffusion model arising from the dynamics of a kind of mosquitos named A. aegypti in Brazil. We first prove the global existence and boundedness of the solutions. Secondly, we establish the threshold type dynamics in terms of the basic reproduction ratio R0. In Chapter 3, we briefly summarize the main results and present some future works.
Author: Harkaran Singh
Publisher: CRC Press
ISBN: 1351251694
Category : Mathematics
Languages : en
Pages : 274
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Book Description
Mankind now faces even more challenging environment- and health-related problems than ever before. Readily available transportation systems facilitate the swift spread of diseases as large populations migrate from one part of the world to another. Studies on the spread of the communicable diseases are very important. This book, Mathematical Population Dynamics and Epidemiology in Temporal and Spatio-Temporal Domains, provides a useful experimental tool for making practical predictions, building and testing theories, answering specific questions, determining sensitivities of the parameters, forming control strategies, and much more. This volume focuses on the study of population dynamics with special emphasis on the migration of populations and the spreading of epidemics among human and animal populations. It also provides the background needed to interpret, construct, and analyze a wide variety of mathematical models. Most of the techniques presented in the book can be readily applied to model other phenomena, in biology as well as in other disciplines.
Author: Fred Brauer
Publisher: Springer Nature
ISBN: 1493998285
Category : Mathematics
Languages : en
Pages : 628
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Book Description
The book is a comprehensive, self-contained introduction to the mathematical modeling and analysis of disease transmission models. It includes (i) an introduction to the main concepts of compartmental models including models with heterogeneous mixing of individuals and models for vector-transmitted diseases, (ii) a detailed analysis of models for important specific diseases, including tuberculosis, HIV/AIDS, influenza, Ebola virus disease, malaria, dengue fever and the Zika virus, (iii) an introduction to more advanced mathematical topics, including age structure, spatial structure, and mobility, and (iv) some challenges and opportunities for the future. There are exercises of varying degrees of difficulty, and projects leading to new research directions. For the benefit of public health professionals whose contact with mathematics may not be recent, there is an appendix covering the necessary mathematical background. There are indications which sections require a strong mathematical background so that the book can be useful for both mathematical modelers and public health professionals.
Author: Bernd Blasius
Publisher: World Scientific
ISBN: 9812771581
Category : Mathematics
Languages : en
Pages : 257
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Book Description
This collection of review articles is devoted to the modeling of ecological, epidemiological and evolutionary systems. Theoretical mathematical models are perhaps one of the most powerful approaches available for increasing our understanding of the complex population dynamics in these natural systems. Exciting new techniques are currently being developed to meet this challenge, such as generalized or structural modeling, adaptive dynamics or multiplicative processes. Many of these new techniques stem from the field of nonlinear dynamics and chaos theory, where even the simplest mathematical rule can generate a rich variety of dynamical behaviors that bear a strong analogy to biological populations.
Author: Horst Malchow
Publisher: Chapman & Hall/CRC
ISBN: 9780367387846
Category : Ecology
Languages : en
Pages : 469
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Book Description
Although the spatial dimension of ecosystem dynamics is now widely recognized, the specific mechanisms behind species patterning in space are still poorly understood and the corresponding theoretical framework is underdeveloped. Going beyond the classical Turing scenario of pattern formation, Spatiotemporal Patterns in Ecology and Epidemiology: Theory, Models, and Simulation illustrates how mathematical modeling and numerical simulations can lead to greater understanding of these issues. It takes a unified approach to population dynamics and epidemiology by presenting several ecoepidemiological models where both the basic interspecies interactions of population dynamics and the impact of an infectious disease are explicitly considered. The book first describes relevant phenomena in ecology and epidemiology, provides examples of pattern formation in natural systems, and summarizes existing modeling approaches. The authors then explore nonspatial models of population dynamics and epidemiology. They present the main scenarios of spatial and spatiotemporal pattern formation in deterministic models of population dynamics. The book also addresses the interaction between deterministic and stochastic processes in ecosystem and epidemic dynamics, discusses the corresponding modeling approaches, and examines how noise and stochasticity affect pattern formation. Reviewing the significant progress made in understanding spatiotemporal patterning in ecological and epidemiological systems, this resource shows that mathematical modeling and numerical simulations are effective tools in the study of population ecology and epidemiology.
Author: Pierre Magal
Publisher: Springer
ISBN: 3540782737
Category : Mathematics
Languages : en
Pages : 314
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Book Description
In this new century mankind faces ever more challenging environmental and publichealthproblems,suchaspollution,invasionbyexoticspecies,theem- gence of new diseases or the emergence of diseases into new regions (West Nile virus,SARS,Anthrax,etc.),andtheresurgenceofexistingdiseases(in?uenza, malaria, TB, HIV/AIDS, etc.). Mathematical models have been successfully used to study many biological, epidemiological and medical problems, and nonlinear and complex dynamics have been observed in all of those contexts. Mathematical studies have helped us not only to better understand these problems but also to ?nd solutions in some cases, such as the prediction and control of SARS outbreaks, understanding HIV infection, and the investi- tion of antibiotic-resistant infections in hospitals. Structuredpopulationmodelsdistinguishindividualsfromoneanother- cording to characteristics such as age, size, location, status, and movement, to determine the birth, growth and death rates, interaction with each other and with environment, infectivity, etc. The goal of structured population models is to understand how these characteristics a?ect the dynamics of these models and thus the outcomes and consequences of the biological and epidemiolo- cal processes. There is a very large and growing body of literature on these topics. This book deals with the recent and important advances in the study of structured population models in biology and epidemiology. There are six chapters in this book, written by leading researchers in these areas.
Author: Zhilan Feng
Publisher: World Scientific
ISBN: 9814522368
Category : Mathematics
Languages : en
Pages : 306
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Book Description
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.
