Age-Structured Population Dynamics in Demography and Epidemiology
This book is the first one in which basic demographic models are rigorously formulated by using modern age-structured population dynamics, extended to study real-world population problems. Age structure is a crucial factor in understanding population phen
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Age-Structured Population Dynamics in Demography and Epidemiology
Age-Structured Population Dynamics in Demography and Epidemiology
Hisashi Inaba
Age-Structured Population Dynamics in Demography and Epidemiology
123
Hisashi Inaba The University of Tokyo Tokyo Japan
ISBN 978-981-10-0187-1 DOI 10.1007/978-981-10-0188-8
ISBN 978-981-10-0188-8
(eBook)
Library of Congress Control Number: 2017930648 © Springer Science+Business Media Singapore 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
To Yoko and Riki
Preface
The main purpose of this book was to explain deterministic, age-structured population dynamics models that appear in demography and epidemiology. The first part of this book addresses pure demographic models, while the second part considers epidemic models for infectious diseases. It should be of essential importance to human beings to know the laws governing their own reproduction and associated results. In fact, the major problems with which we have been confronted relate to population dynamics, as was clearly recognized by Thomas Robert Malthus in the eighteenth century. From the beginning, the main concerns of demography have extended beyond the variations in population size and distribution to the age structure dynamics of the population. The starting point of modern demography was the life table technique developed to measure human life expectancy in the seventeenth century. In the eighteenth century, Euler developed a difference equation model for human populations to show that an age-structured population with constant fertility and mortality will grow geometrically. Moreover, Euler derived r
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