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" Mathematical models in epidemiology / "
Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng.
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BL
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| Record Number
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851780
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| Main Entry
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Brauer, Fred
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| Title & Author
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Mathematical models in epidemiology /\ Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng.
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| Publication Statement
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New York, NY :: Springer,, 2019.
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| Series Statement
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Texts in applied mathematics,; volume 69
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1 online resource (xvii, 619 pages) :: illustrations (some color)
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| ISBN
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1493998285
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: 9781493998289
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1493998269
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9781493998265
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Includes bibliographical references and index.
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| Contents
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Intro; Foreword; Preface; Acknowledgments; Contents; Part I Basic Concepts of Mathematical Epidemiology; 1 Introduction: A Prelude to Mathematical Epidemiology; 1.1 Introduction; 1.2 Some History; 1.2.1 The Beginnings of Compartmental Models; 1.2.2 Stochastic Models; 1.2.3 Developments in Compartmental Models; 1.2.4 Endemic Disease Models; 1.2.5 Diseases Transmitted by Vectors; 1.2.6 Heterogeneity of Mixing; 1.3 Strategic Models and This Volume; References; 2 Simple Compartmental Models for Disease Transmission; 2.1 Introduction to Compartmental Models; 2.2 The SIS Model
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2.3 The SIR Model with Births and Deaths2.4 The Simple Kermack-McKendrick Epidemic Model; 2.5 Epidemic Models with Deaths due to Disease; 2.6 *Project: Discrete Epidemic Models; 2.7 *Project: Pulse Vaccination; 2.8 *Project: A Model with Competing Disease Strains; 2.9 Project: An Epidemic Model in Two Patches; 2.10 Project: Fitting Data for an Influenza Model; 2.11 Project: Social Interactions; 2.12 Exercises; References; 3 Endemic Disease Models; 3.1 More Complicated Endemic Disease Models; 3.1.1 Exposed Periods; 3.1.2 A Treatment Model; 3.1.3 Vertical Transmission
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3.2 Some Applications of the SIR Model3.2.1 Herd Immunity; 3.2.2 Age at Infection; 3.2.3 The Inter-Epidemic Period; 3.2.4 ``Epidemic'' Approach to Endemic Equilibrium; 3.3 Temporary Immunity; 3.3.1 *Delay in an SIRS Model; 3.4 A Simple Model with Multiple Endemic Equilibria; 3.5 A Vaccination Model: Backward Bifurcations; 3.5.1 The Bifurcation Curve; 3.6 *An SEIR Model with General Disease Stage Distributions; 3.6.1 *Incorporation of Quarantine and Isolation; 3.6.2 *The Reduced Model of (3.42) Under GDA; 3.6.3 *Comparison of EDM and GDM; 3.7 Diseases in Exponentially Growing Populations
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3.8 Project: Population Growth and Epidemics3.9 *Project: An Environmentally Driven Infectious Disease; 3.10 *Project: A Two-Strain Model with Cross Immunity; 3.11 Exercises; References; 4 Epidemic Models; 4.1 A Branching Process Disease Outbreak Model; 4.1.1 Transmissibility; 4.2 Network and Compartmental Epidemic Models; 4.3 More Complicated Epidemic Models; 4.3.1 Exposed Periods; 4.3.2 A Treatment Model; 4.3.3 An Influenza Model; 4.3.4 A Quarantine-Isolation Model; 4.4 An SIR Model with a General Infectious Period Distribution; 4.5 The Age of Infection Epidemic Model
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4.5.1 A General SEIR Model4.5.2 A General Treatment Model; 4.5.3 A General Quarantine/Isolation Epidemic Model; 4.6 The Gamma Distribution; 4.7 Interpretation of Data and Parametrization; 4.7.1 Models of SIR Type; 4.7.2 Models of SEIR Type; 4.7.3 Mean Generation Time; 4.8 *Effect of Timing of Control Programs on EpidemicFinal Size; 4.9 Directions for Generalization; 4.10 Some Warnings; 4.11 *Project: A Discrete Model with Quarantine and Isolation; 4.12 Project: Epidemic Models with Direct and IndirectTransmission; 4.13 Exercises; References; 5 Models with Heterogeneous Mixing
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| Abstract
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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.
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| Subject
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Epidemiology-- Mathematical models.
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| Subject
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Epidemiology-- Mathematical models.
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| Dewey Classification
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614.4015/118
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| LC Classification
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RA652.2.M3
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| Added Entry
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Castillo-Chávez, Carlos
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Feng, Zhilan,1959-
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