Matrix Models for Population, Disease, and Evolutionary Dynamics: 106 (Student Mathematical Library) - Softcover

J. M. Cushing (author)

Softcover

ISBN 10: 1470473348 ISBN 13: 9781470473341

Publisher: American Mathematical Society, 2024

Synopsis

This book offers an introduction to the use of matrix theory and linear algebra in modeling the dynamics of biological populations. Matrix algebra has been used in population biology since the 1940s and continues to play a major role in theoretical and applied dynamics for populations structured by age, body size or weight, disease states, physiological and behavioral characteristics, life cycle stages, or any of many other possible classification schemes. With a focus on matrix models, the book requires only first courses in multi-variable calculus and matrix theory or linear algebra as prerequisites.

The reader will learn the basics of modeling methodology (i.e., how to set up a matrix model from biological underpinnings) and the fundamentals of the analysis of discrete time dynamical systems (equilibria, stability, bifurcations, etc.). A recurrent theme in all chapters concerns the problem of extinction versus survival of a population. In addition to numerous examples that illustrate these fundamentals, several applications appear at the end of each chapter that illustrate the full cycle of model setup, mathematical analysis, and interpretation. The author has used the material over many decades in a variety of teaching and mentoring settings, including special topics courses and seminars in mathematical modeling, mathematical biology, and dynamical systems.

About this title

About the Author

J. M. Cushing, University of Arizona, Tucson, AZ.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2024
• Language: English
• ISBN 10: 1470473348
• ISBN 13: 9781470473341
• Binding: Paperback
• Number of pages: 305