Stochastic Population Models: A Compartmental Perspective

ISBN-13: 9780387986579 / Angielski / Miękka / 2000 / 202 str.

James H. Matis; J. H. Matis; T. R. Kiffe

Opis

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 stochastic basis for our ecological modeling efforts. The other is the third edition of Jacquez' 28] classic book on compartmental analysis. He reviews stochastic 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 stochastic com partmental modeling with our more recent research focusing on stochastic 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 stochastic population models. In accordance with this objective, we have chosen to illustrate the various stochastic models, using four primary applications described in Chapter 2. In so doing, this mono graph is based largely on our own published work."

Recenzje

"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 stochastic population models." (P.R.Parthasarathy, zbMATH 0943.92029, 2022)

Spis treści

I Introduction.- 1. Overview of Models.- 1.1 Modeling Objectives.- 1.2 Structure of Monograph.- 2. Some Applications.- 2.1 Introduction.- 2.2 Application to Invasion of Africanized Honey Bee.- 2.3 Application to Muskrat Spread in the Netherlands.- 2.4 Application to Bioaccumulation of Mercury in Fish.- 2.5 Application to Human Calcium Kinetics.- II Models for a Single Population.- 3. Basic Methodology for Single Population Stochastic Models.- 3.1 Introduction.- 3.2 Basic Assumptions.- 3.3 Moments and Cumulants.- 3.4 Kolmogorov Differential Equations.- 3.5 Generating Functions.- 3.6 Partial Differential Equations for Generating Functions.- 3.7 General Approach to Single Population Growth Models.- 4. Linear Immigration-Death Models.- 4.1 Introduction.- 4.2 Deterministic Model.- 4.3 Probability Distributions for the Stochastic Model.- 4.4 Generating Functions.- 4.5 Cumulant Functions.- 4.6 Some Properties of the Stochastic Solution.- 4.7 Illustrations.- 5. Linear Birth-Immigration-Death Models.- 5.1 Introduction.- 5.2 Deterministic Model.- 5.3 Probability Distribution for the Stochastic Model.- 5.4 Generating Functions.- 5.5 Cumulant Functions.- 5.6 Some Properties of the Stochastic Solution.- 5.7 Illustrations.- 6. Nonlinear Birth-Death Models.- 6.1 Introduction.- 6.2 Deterministic Model.- 6.3 Probability Distributions for the Stochastic Model.- 6.4 Generating Functions.- 6.5 Cumulant Functions.- 6.6 Some Properties of the Stochastic Solution.- 6.7 Illustrations.- 6.8 Appendices.- III Models for Multiple Populations.- 7. Nonlinear Birth-Immigration-Death Models.- 7.1 Introduction.- 7.2 Deterministic Model.- 7.3 Probability Distribution for the Stochastic Model.- 7.4 Generating Functions.- 7.5 Cumulant Functions.- 7.6 Some Properties of the Stochastic Solution.- 7.7 Illustrations.- 7.8 Appendices.- 8. Standard Multiple Compartment Analysis.- 8.1 Introduction.- 8.2 Deterministic Model Formulation and Solution.- 8.3 Illustrations.- 9. Basic Methodology for Multiple Population Stochastic Models.- 9.1 Introduction.- 9.2 Basic Assumptions.- 9.3 Joint Moments and Cumulants.- 9.4 Kolmogorov Differential Equations.- 9.5 Bivariate Generating Functions.- 9.6 Partial Differential Equations for Generating Functions.- 9.7 General Approach to Multiple Population Growth Models.- 10. Linear Death-Migration Models.- 10.1 Introduction.- 10.2 General Formulation of the Stochastic Model.- 10.3 Direct Solution for Stochastic Migration-Death Model.- 10.4 Mean Residence Times.- 10.5 Appendix.- 11. Linear Immigration-Death-Migration Models.- 11.1 Introduction.- 11.2 Generating Functions for the Stochastic Model.- 11.3 Probability Distribution.- 11.4 Cumulant Functions.- 12. Linear Birth-Immigration-Death-Migration Models.- 12.1 Introduction.- 12.2 Equations for Cumulant Functions.- 12.3 Application to Dispersal of African Bees-Basic Model.- 12.4 Application to Muskrat Spread Data.- 12.5 Appendix.- 13. Nonlinear Birth-Death-Migration Models.- 13.1 Introduction.- 13.2 Probability Distribution for the Stochastic Model.- 13.3 Cumulant Functions.- 14. Nonlinear Host-Parasite Models.- 14.1 Introduction.- 14.2 Proposed Host-Parasite Model.- 14.3 Conclusions and Future Research Directions.- 14.4 Appendix.- References.