Stochastic Population Models: A Compartmental Perspective

by James H. Matis, Thomas R. Kiffe

Overview

This monograph has been heavily influenced by two books. One is Ren­ shaw's [82] work on modeling biological populations in space and time. It was published as we were busily engaged in modeling African bee dispersal, and provided strong affirmation for the shastic basis for our ecological modeling efforts. The other is the third edition of Jacquez' [28] classic book on compartmental analysis. He reviews shastic compartmental analysis and utilizes generating functions in this edition to derive many useful re­ sults. We interpreted Jacquez' use of generating functions as a message that the day had come for modeling practioners to consider using this powerful approach as a model-building tool. We were inspired by the idea of using generating functions and related methods for two purposes. The first is to integrate seamlessly our previous research centering in shastic com­ partmental modeling with our more recent research focusing on shastic population modeling. The second, related purpose is to present some key research results of practical application in a natural, user-friendly way to the large user communities of compartmental and biological population modelers. One general goal of this monograph is to make a case for the practical utility of the various shastic population models. In accordance with this objective, we have chosen to illustrate the various shastic models, using four primary applications described in Chapter 2. In so doing, this monograph is based largely on our own published work.

Product Details

ISBN-13:	9780387986579
Publisher:	Springer New York
Publication date:	06/15/2000
Series:	Lecture Notes in Statistics , #145
Edition description:	Softcover reprint of the original 1st ed. 2000
Pages:	202
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

I Introduction.- 1. Overview of Models.- 2. Some Applications.- II Models for a Single Population.- 3. Basic Methodology for Single Population Shastic Models.- 4. Linear Immigration-Death Models.- 5. Linear Birth-Immigration-Death Models.- 6. Nonlinear Birth-Death Models.- III Models for Multiple Populations.- 7. Nonlinear Birth-Immigration-Death Models.- 8. Standard Multiple Compartment Analysis.- 9. Basic Methodology for Multiple Population Shastic Models.- 10. Linear Death-Migration Models.- 11. Linear Immigration-Death-Migration Models.- 12. Linear Birth-Immigration-Death-Migration Models.- 13. Nonlinear Birth-Death-Migration Models.- 14. Nonlinear Host-Parasite Models.- References.

Editorial Reviews

Models are illustrated with numerous practical applications. … The reviewer enjoyed reading this book which will be immensely useful to mathematicians and statisticians interested in biological modelling. Due to the attractive topics as well as the informal and vivid style often used in the presentation and description of the challenging biological problems, they will find this book absorbing and will benefit a lot from it. It is a valuable addition to the existing line of books on shastic population models.” (P.R.Parthasarathy, zbMATH 0943.92029, 2022)

From the Publisher