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.
Inhalt
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.