Global Dynamics of Some Spatially Heterogeneous Population Models PDF Download
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Author: Fang Zhang
Publisher:
ISBN:
Category : Dynamics
Languages : en
Pages : 0
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Author: Fang Zhang
Publisher:
ISBN:
Category : Dynamics
Languages : en
Pages : 0
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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: Ruiwen Wu
Publisher:
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Category :
Languages : en
Pages :
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Spatial and/or temporal evolutions are very important topics in epidemiology and ecology. This thesis is devoted to the study of the global dynamics of some population models incorporating with environmental heterogeneities. Vector-borne diseases such as West Nile virus and malaria, pose a threat to public health worldwide. Both vector life cycle and parasite development are highly sensitive to climate factors. To understand the role of seasonality on disease spread, we start with a periodic West Nile virus transmission model with time-varying incubation periods. Apart from seasonal variations, another important feature of our environment is the spatial heterogeneity. Hence, we incorporate the movement of both vectors and hosts, temperature-dependent incubation periods, seasonal fluctuations and spatial heterogeneity into a general reaction-diffusion vector-borne disease model. By using the theory of basic reproduction number, R0, and the theory of infinite dimensional dynamical systems, we derive R0 and establish a threshold-type result for the global dynamics in terms of R0 for each model. As biological invasions have significant impacts on ecology and human society, how the growth and spatial spread of invasive species interact with environment becomes an important and challenging problem. We first propose an impulsive integro-differential model to describe a single invading species with a birth pulse in the reproductive stage and a nonlocal dispersal stage. Next, we study the propagation dynamics for a class of integro-difference two-species competition models in a spatially periodic habitat.
Author: Xiao Yu
Publisher:
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Category :
Languages : en
Pages :
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This thesis is devoted to the study of the global dynamics of some reaction and diffusion models incorporating with spatial and/or temporal heterogeneities. We first investigate the spatial dynamics of a reaction-advection-diffusion model for a stream population in a time-periodic environment. Then we explore the propagation phenomena for a Lotka-Volterra reaction-advection-diffusion competition model in a periodic habitat. Moreover, we establish the theory of traveling waves and spreading speeds for time-space periodic monotone semiflows with monostable structure and apply it to a time-space version of the two-species competition model. To understand the effects of the spatial heterogeneity on the spread of Lyme disease, we propose a nonlocal and time-delayed reaction-diffusion model and obtain the global stability in terms of the basic reproduction ratio and the spreading speed of the disease. At the end of this thesis, some interesting problems are presented for further investigation.
Author: Yuxiang Zhang
Publisher:
ISBN:
Category : Population biology
Languages : en
Pages : 0
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Author: David T. McArdle
Publisher:
ISBN:
Category : Differnce equations
Languages : en
Pages : 274
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Author: Alun Lewis Lloyd
Publisher:
ISBN:
Category : Animal populations
Languages : en
Pages : 175
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Author: Dongmei Chen
Publisher: John Wiley & Sons
ISBN: 1118629914
Category : Medical
Languages : en
Pages : 496
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Book Description
Features modern research and methodology on the spread of infectious diseases and showcases a broad range of multi-disciplinary and state-of-the-art techniques on geo-simulation, geo-visualization, remote sensing, metapopulation modeling, cloud computing, and pattern analysis Given the ongoing risk of infectious diseases worldwide, it is crucial to develop appropriate analysis methods, models, and tools to assess and predict the spread of disease and evaluate the risk. Analyzing and Modeling Spatial and Temporal Dynamics of Infectious Diseases features mathematical and spatial modeling approaches that integrate applications from various fields such as geo-computation and simulation, spatial analytics, mathematics, statistics, epidemiology, and health policy. In addition, the book captures the latest advances in the use of geographic information system (GIS), global positioning system (GPS), and other location-based technologies in the spatial and temporal study of infectious diseases. Highlighting the current practices and methodology via various infectious disease studies, Analyzing and Modeling Spatial and Temporal Dynamics of Infectious Diseases features: Approaches to better use infectious disease data collected from various sources for analysis and modeling purposes Examples of disease spreading dynamics, including West Nile virus, bird flu, Lyme disease, pandemic influenza (H1N1), and schistosomiasis Modern techniques such as Smartphone use in spatio-temporal usage data, cloud computing-enabled cluster detection, and communicable disease geo-simulation based on human mobility An overview of different mathematical, statistical, spatial modeling, and geo-simulation techniques Analyzing and Modeling Spatial and Temporal Dynamics of Infectious Diseases is an excellent resource for researchers and scientists who use, manage, or analyze infectious disease data, need to learn various traditional and advanced analytical methods and modeling techniques, and become aware of different issues and challenges related to infectious disease modeling and simulation. The book is also a useful textbook and/or supplement for upper-undergraduate and graduate-level courses in bioinformatics, biostatistics, public health and policy, 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: David Tilman
Publisher: Princeton University Press
ISBN: 069118836X
Category : Science
Languages : en
Pages : 368
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Book Description
Spatial Ecology addresses the fundamental effects of space on the dynamics of individual species and on the structure, dynamics, diversity, and stability of multispecies communities. Although the ecological world is unavoidably spatial, there have been few attempts to determine how explicit considerations of space may alter the predictions of ecological models, or what insights it may give into the causes of broad-scale ecological patterns. As this book demonstrates, the spatial structure of a habitat can fundamentally alter both the qualitative and quantitative dynamics and outcomes of ecological processes. Spatial Ecology highlights the importance of space to five topical areas: stability, patterns of diversity, invasions, coexistence, and pattern generation. It illustrates both the diversity of approaches used to study spatial ecology and the underlying similarities of these approaches. Over twenty contributors address issues ranging from the persistence of endangered species, to the maintenance of biodiversity, to the dynamics of hosts and their parasitoids, to disease dynamics, multispecies competition, population genetics, and fundamental processes relevant to all these cases. There have been many recent advances in our understanding of the influence of spatially explicit processes on individual species and on multispecies communities. This book synthesizes these advances, shows the limitations of traditional, non-spatial approaches, and offers a variety of new approaches to spatial ecology that should stimulate ecological research.
