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" Mathematical population : "
Harkaran Singh, PhD, Joydip Dhar, PhD.
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BL
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| Record Number
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844877
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| Main Entry
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Singh, Harkaran.
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| Title & Author
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Mathematical population : : dynamics and epidemiology in temporal and spatio-temporal domains /\ Harkaran Singh, PhD, Joydip Dhar, PhD.
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| Publication Statement
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Toronto ;New Jersey :: Apple Academic Press,, 2018.
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1 online resource
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| ISBN
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1351251686
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: 1351251694
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: 1351251708
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: 9781351251686
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: 9781351251693
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: 9781351251709
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9781771886710
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Includes bibliographical references and index.
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| Contents
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Cover; Half Title; Title; Copyright; Dedication; Contents; About the Authors; List of Figures; List of Tables; List of Symbols; Preface; Chapter 1 Introduction and Mathematical Preliminaries; 1.1 Introduction; 1.1.1 Population Dynamics; 1.1.2 Prey-Predator Interactions; 1.1.3 Discrete Generations; 1.1.4 Diffusion of Population; 1.1.5 Patchy Environment; 1.1.6 Epidemiology; 1.1.7 Eco-Epidemiology; 1.1.8 Stage-Structure; 1.1.9 Time Delay; 1.1.10 Disease Acquired Immunity; 1.1.11 Vaccine Induced Immunity; 1.1.12 Non-Pharmaceutical Interventions (NPIs) Through Media Awareness
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1.2 Mathematical Preliminaries1.2.1 Equilibria of Temporal System; 1.2.2 Nature of Roots; 1.2.3 Stability of Equilibrium Points; 1.2.4 Lyapunov's Direct Method; 1.2.5 Bifurcation in Continuous System; 1.2.6 Euler's Scheme for Discretization; 1.2.7 Stability of Fixed Points in Discrete System; 1.2.8 Center Manifold in Discrete System; 1.2.9 Bifurcation in Discrete System; 1.2.10 Next Generation Operator Method; 1.2.11 Sensitivity Analysis; 1.3 Summary; Chapter 2 Discrete-Time Bifurcation Behavior of a Prey-Predator System with Generalized Predator; 2.1 Introduction
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2.2 Formulation of Mathematical Model-12.3 Discrete Dynamical Behavior of Model-1; 2.3.1 Flip Bifurcation; 2.3.2 Hopf Bifurcation; 2.4 Formulation of Mathematical Model-2; 2.5 Discrete Dynamical Behavior of Model-2; 2.5.1 Flip Bifurcation; 2.5.2 Hopf Bifurcation; 2.6 Numerical Simulations; 2.7 Summary; Chapter 3 A Single Species Harvesting Model with Diffusion in a Two- Patch Habitat; 3.1 Introduction; 3.2 Formulation of Mathematical Model; 3.3 The Analysis of the Model; 3.3.1 Under Reservoir Boundary Conditions; 3.3.2 Under No-Flux Boundary Conditions
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3.3.3 The Case of Uniform Equilibrium State3.4 Summary; Chapter 4 A Single Species Model with Supplementary Forest Resource in a Two-Patch Habitat; 4.1 Introduction; 4.2 Formulation of Mathematical Model; 4.3 Analysis of the Model in a Homogeneous Habitat; 4.3.1 Model without Diffusion; 4.3.2 Model with Diffusion; 4.4 Analysis of the Model with Diffusion in a Two-Patch Habitat; 4.5 A Particular Case; 4.6 When the Species Population is Uniform Throughout the Habitat; 4.7 Summary; Chapter 5 A Two Competing Species Model with Diffusion in a Homo-geneous and Two-Patch Forest Habitats
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5.1 Introduction5.2 Formulation of Mathematical Model; 5.3 Analysis of the Model in a Homogeneous Habitat; 5.3.1 Model without Diffusion; 5.3.2 Model with Diffusion; 5.4 Analysis of the Model with Diffusion in a Two-Patch Habitat; 5.4.1 The Uniform Equilibrium State Under Both Sets of Boundary Conditions; 5.4.2 The Non-Uniform Equilibrium State; 5.4.3 The Model Under the Reservoir Boundary Conditions:When x 2> x 1 and y 2> y 1:; 5.4.4 The Model Under No-Flux Boundary Conditions; 5.4.5 Both the Species have Uniform Steady State in the Second Patch; 5.5 Summary
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| Abstract
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"In todays era, the spread of diseases happens very quickly as a large population migrates from one part to another of the world with the readily available transportation facilities. In this century, mankind faces even more challenging environment- and health-related problems than ever before. Therefore, the 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 in making practical predictions, building and testing theories, answering specific questions, determining sensitivities of the parameters, devising control strategies, and much more. This new volume, Mathematical Population Dynamics and Epidemiology in Temporal and Spatio-Temporal Domains, focuses on the study of population dynamics with special emphasis on the migration of populations in a heterogeneous patchy habitat, the human and animal population, and the spreading of epidemics, an important area of research in mathematical biology dealing with the survival of different species. The volume 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. The studies presented here on the prey-predator models can be helpful for conservation strategies in forestry habitats, and the epidemic model studies can helpful to the public health policymakers in determining how to control the rapid outbreak of infectious diseases. In this book, the authors have proposed eleven different models in order to facilitate understanding: Two models with different prey-predator interactionsFour population models with diffusion in two-patch environmentOne prey-predator model with disease in the preyFour epidemic models with different control strategies. This book will be of interest to interdisciplinary researchers and policymakers, especially mathematical biologists, biologists, physicists, and epidemiologists. The book can be useful as textbook or reference book for graduate and postgraduate advanced level mathematical biology courses."--Provided by publisher.
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| Subject
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Epidemics-- Mathematical models.
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Epidemiology-- Statistical methods.
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Epidemiology-- statistics numerical data.
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Epidemics-- Mathematical models.
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Epidemiology-- Statistical methods.
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MEDICAL-- Forensic Medicine.
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MEDICAL-- Preventive Medicine.
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MEDICAL-- Public Health.
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| Dewey Classification
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614.4072/7
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| LC Classification
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RA652.2.M3
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| NLM classification
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WA 950
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cci1icclacc
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coll13lacc
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| Added Entry
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Dhar, Joydip.
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