Ebook: Stochastic Population Models: A Compartmental Perspective
- Tags: Statistical Theory and Methods
- Series: Lecture Notes in Statistics 145
- Year: 2000
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
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.
The book focuses on stochastic modeling of population processes. The book presents new symbolic mathematical software to develop practical methodological tools for stochastic population modeling. The book assumes calculus and some knowledge of mathematical modeling, including the use of differential equations and matrix algebra.
The book focuses on stochastic modeling of population processes. The book presents new symbolic mathematical software to develop practical methodological tools for stochastic population modeling. The book assumes calculus and some knowledge of mathematical modeling, including the use of differential equations and matrix algebra.
Content:
Front Matter....Pages i-x
Front Matter....Pages 1-1
Overview of Models....Pages 2-4
Some Applications....Pages 5-15
Front Matter....Pages 15-15
Basic Methodology for Single Population Stochastic Models....Pages 17-29
Linear Immigration-Death Models....Pages 30-39
Linear Birth-Immigration-Death Models....Pages 40-48
Nonlinear Birth-Death Models....Pages 49-71
Front Matter....Pages 100-100
Nonlinear Birth-Immigration-Death Models....Pages 72-99
Standard Multiple Compartment Analysis with the Deterministic Model....Pages 101-109
Basic Methodology for Multiple Population Stochastic Models....Pages 110-118
Linear Death-Migration Models....Pages 119-136
Linear Immigration-Death-Migration Models....Pages 137-141
Linear Birth-Immigration-Death Migration Models....Pages 142-160
Nonlinear Birth-Death-Migration Models....Pages 161-171
Nonlinear Host-Parasite Models....Pages 172-188
Back Matter....Pages 189-204
The book focuses on stochastic modeling of population processes. The book presents new symbolic mathematical software to develop practical methodological tools for stochastic population modeling. The book assumes calculus and some knowledge of mathematical modeling, including the use of differential equations and matrix algebra.
Content:
Front Matter....Pages i-x
Front Matter....Pages 1-1
Overview of Models....Pages 2-4
Some Applications....Pages 5-15
Front Matter....Pages 15-15
Basic Methodology for Single Population Stochastic Models....Pages 17-29
Linear Immigration-Death Models....Pages 30-39
Linear Birth-Immigration-Death Models....Pages 40-48
Nonlinear Birth-Death Models....Pages 49-71
Front Matter....Pages 100-100
Nonlinear Birth-Immigration-Death Models....Pages 72-99
Standard Multiple Compartment Analysis with the Deterministic Model....Pages 101-109
Basic Methodology for Multiple Population Stochastic Models....Pages 110-118
Linear Death-Migration Models....Pages 119-136
Linear Immigration-Death-Migration Models....Pages 137-141
Linear Birth-Immigration-Death Migration Models....Pages 142-160
Nonlinear Birth-Death-Migration Models....Pages 161-171
Nonlinear Host-Parasite Models....Pages 172-188
Back Matter....Pages 189-204
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