Stochastic Population Models

1. Front Matter

   Pages i-x

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2. Introduction

   1. Front Matter

      Pages 1-1

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   2. Overview of Models

      • James H. Matis, Thomas R. Kiffe

      Pages 2-4

   3. Some Applications

      • James H. Matis, Thomas R. Kiffe

      Pages 5-15

3. Models for a Single Population

   1. Front Matter

      Pages 15-15

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   2. Basic Methodology for Single Population Stochastic Models

      • James H. Matis, Thomas R. Kiffe

      Pages 17-29

   3. Linear Immigration-Death Models

      • James H. Matis, Thomas R. Kiffe

      Pages 30-39

   4. Linear Birth-Immigration-Death Models

      • James H. Matis, Thomas R. Kiffe

      Pages 40-48

   5. Nonlinear Birth-Death Models

      • James H. Matis, Thomas R. Kiffe

      Pages 49-71

4. Models for Multiple Populations

   1. Front Matter

      Pages 100-100

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   2. Nonlinear Birth-Immigration-Death Models

      • James H. Matis, Thomas R. Kiffe

      Pages 72-99

   3. Standard Multiple Compartment Analysis with the Deterministic Model

      • James H. Matis, Thomas R. Kiffe

      Pages 101-109

   4. Basic Methodology for Multiple Population Stochastic Models

      • James H. Matis, Thomas R. Kiffe

      Pages 110-118

   5. Linear Death-Migration Models

      • James H. Matis, Thomas R. Kiffe

      Pages 119-136

   6. Linear Immigration-Death-Migration Models

      • James H. Matis, Thomas R. Kiffe

      Pages 137-141

   7. Linear Birth-Immigration-Death Migration Models

      • James H. Matis, Thomas R. Kiffe

      Pages 142-160

   8. Nonlinear Birth-Death-Migration Models

      • James H. Matis, Thomas R. Kiffe

      Pages 161-171

   9. Nonlinear Host-Parasite Models

      • James H. Matis, Thomas R. Kiffe

      Pages 172-188

5. Back Matter

   Pages 189-204

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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.

• Mathematica
• Moment
• bee
• calculus
• differential equation
• equation
• mathematical modeling
• mathematical software
• migration
• modeling
• population
• probability
• probability distribution
• software
• tool

“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)

• Department of Statistics, Texas A&M University, College Station, USA

  James H. Matis

• Department of Mathematics, Texas A&M University, College Station, USA

  Thomas R. Kiffe

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