The basic approach to age-structured population dynamics : models, methods and numerics

✍ Scribed by Iannelli, Mimmo; Milner, Fabio

• Publisher: Springer Verlag
• Year: 2017
• Tongue: English
• Leaves: 357
• Series: Lecture notes on mathematical modelling in the life sciences
• Category: Library

✦ Synopsis

This book provides an introduction to age-structured population modeling which emphasises 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 modelling to the spread of diseases and epidemics while also addressing the issue of regularity of solutions, the asymptotic behaviour 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. Read more...

Abstract: This book provides an introduction to age-structured population modeling which emphasises 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 modelling to the spread of diseases and epidemics while also addressing the issue of regularity of solutions, the asymptotic behaviour 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

✦ Table of Contents

Front Matter ....Pages i-xii
Why Age Structure? An Introduction (Mimmo Iannelli, Fabio Milner)....Pages 1-48
The Basic Linear Theory (Mimmo Iannelli, Fabio Milner)....Pages 49-87
Numerical Methods for the Linear Model (Mimmo Iannelli, Fabio Milner)....Pages 89-122
The Time-Dependent Case (Mimmo Iannelli, Fabio Milner)....Pages 123-140
Nonlinear Models (Mimmo Iannelli, Fabio Milner)....Pages 141-172
Stability of Equilibria (Mimmo Iannelli, Fabio Milner)....Pages 173-200
Numerical Methods for the Nonlinear Model (Mimmo Iannelli, Fabio Milner)....Pages 201-217
Global Behavior (Mimmo Iannelli, Fabio Milner)....Pages 219-240
Class-Age Structure for Epidemics (Mimmo Iannelli, Fabio Milner)....Pages 241-276
Epidemics and Demography (Mimmo Iannelli, Fabio Milner)....Pages 277-319
Back Matter ....Pages 321-350

✦ Subjects

Age distribution (Demography);Population -- Mathematical models;Demography -- Mathematical models;SOCIAL SCIENCE / Discrimination & Race Relations;SOCIAL SCIENCE / Minority Studies