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 phenomena, and the essential ideas in demography and epidemiology cannot be understood without mathematical formulation; therefore, this book gives readers a robust mathematical introduction to human population studies. In the first part of the volume, classical demographic models such as the stable population model and its linear extensions, density-dependent nonlinear models, and pair-formation models are formulated by the McKendrick partial differential equation and are analyzed from a dynamical system point of view. In the second part, mathematical models for infectious diseases spreading at the population level are examined by using nonlinear differential equations and a renewal equation. Since an epidemic can be seen as a nonlinear renewal process of an infected population, this book will provide a natural unification point of view for demography and epidemiology. The well-known epidemic threshold principle is formulated by the basic reproduction number, which is also a most important key index in demography. The author develops a universal theory of the basic reproduction number in heterogeneous environments. By introducing the host age structure, epidemic models are developed into more realistic demographic formulations, which are essentially needed to attack urgent epidemiological control problems in the real world.

This book provides an introduction to age-structured population modeling which emphasizes the connection between mathematical theory and underlying biological assumptions. Through the rigorous development of the linear theory and the nonlinear theory alongside numerics, the authors explore classical equations that describe the dynamics of certain ecological systems. Modeling aspects are discussed to show how relevant problems in the fields of demography, ecology and epidemiology can be formulated and treated within the theory. In particular, the book presents extensions of age-structured modeling to the spread of diseases and epidemics while also addressing the issue of regularity of solutions, the asymptotic behavior of solutions, and numerical approximation. With sections on transmission models, non-autonomous models and global dynamics, this book fills a gap in the literature on theoretical population dynamics. The Basic Approach to Age-Structured Population Dynamics will appeal to graduate students and researchers in mathematical biology, epidemiology and demography who are interested in the systematic presentation of relevant models and mathematical methods.

Interest in the temporal fluctuations of biological populations can be traced to the dawn of civilization. How can mathematics be used to gain an understanding of population dynamics? This monograph introduces the theory of structured population dynamics and its applications, focusing on the asymptotic dynamics of deterministic models. This theory bridges the gap between the characteristics of individual organisms in a population and the dynamics of the total population as a whole. In this monograph, many applications that illustrate both the theory and a wide variety of biological issues are given, along with an interdisciplinary case study that illustrates the connection of models with the data and the experimental documentation of model predictions. The author also discusses the use of discrete and continuous models and presents a general modeling theory for structured population dynamics. Cushing begins with an obvious point: individuals in biological populations differ with regard to their physical and behavioral characteristics and therefore in the way they interact with their environment. Studying this point effectively requires the use of structured models. Specific examples cited throughout support the valuable use of structured models. Included among these are important applications chosen to illustrate both the mathematical theories and biological problems that have received attention in recent literature.

The material of the present book is an extension of a graduate course given by the author at the University "Al.I. Cuza" Iasi and is intended for stu dents and researchers interested in the applications of optimal control and in mathematical biology. Age is one of the most important parameters in the evolution of a bi ological population. Even if for a very long period age structure has been considered only in demography, nowadays it is fundamental in epidemiology and ecology too. This is the first book devoted to the control of continuous age structured populationdynamics.It focuses on the basic properties ofthe solutions and on the control of age structured population dynamics with or without diffusion. The main goal of this work is to familiarize the reader with the most important problems, approaches and results in the mathematical theory of age-dependent models. Special attention is given to optimal harvesting and to exact controllability problems, which are very important from the econom ical or ecological points of view. We use some new concepts and techniques in modern control theory such as Clarke's generalized gradient, Ekeland's variational principle, and Carleman estimates. The methods and techniques we use can be applied to other control problems.

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.

A Primer of Population Dynamics introduces to the basics of population studies. Author Krishnan Namboodiri utilizes a question-and-answer format that explores topics such as population theories and conceptual schemes, demographic data, mortality, fertility, migration, family and household, food production, and the environment and much more. Questions are accompanied by detailed explanations as well as references for additional information. An extensive index and glossary allow for easy retrieval of information. This introductory textbook is written for students studying demography, population, sociology, and public health.

With this book, Siegel, an internationally known demographer and gerontologist, has made a unique contribution to the fledgling fields of health demography, and the demography and epidemiology of aging. The book represents a felicitous union of epidemiology, gerontology, and demography, and appears to be the first and only comprehensive text on this subject now available. Drawing on a wide range of sciences in addition to demography, gerontology, and epidemiology, including medical sociology, biostatistics, public policy, bioethics, and molecular biology, the author treats theoretical and applied issues, links methods and findings, covers the material internationally, nationally, and locally, and while focusing on the elderly, treats the entire life course. The methods, materials, and pespectives of demography and epidemiology are brought to bear on such topics as the prospects for future increases in human longevity, the relative contribution of life style, environment, genetics, and chance in human longevity, the measurement of the share of healthy years in total life expectancy, the role of population growth in the rising costs of health care, and the applications of health demography in serving the health needs of local communities. The separate chapters systematically develop the topics of the sources and quality of health data; mortality, life tables, and the measurement of health status; the interrelationships of health, on the one hand, and mortality, fertility, migration, and age structure, on the other; health conditions in the less developed countries; the concepts and theories of aging and projections of the aged population; and local health applications, public health policy, and bioethical issues in health demography. Given its comprehensiveness, clarity, interdisciplinary scope, and authencity, this book appeals to a wide range of users, from students and teachers of medical sociology, the demography of aging, and public health studies to practitioners in these areas, both as a text in health demography and the demography/epidemiology of aging, and as a reference work in these fields.

This book provides new theories, applications and quantitative methods in demography, population studies and statistics. It presents and applies data analysis, statistics and stochastic modeling techniques focusing on demography, population aging, mortality and health sciences. The book describes diverse stochastic processes as well as Markov and semi-Markov models in demography and population studies, along with chapters on statistical models and methods in biostatistics and epidemiology. As such the book will be a valuable source to demographers, health scientists, statisticians, economists and sociologists.