Student Mathematical Library: Matrix Models for Population, Disease, and Evolutionary Dynamics by J. M. Cushing (2024, Trade Paperback)

American Mathematical Society

1470473348

9781470473341

8064786587

305 Pages

Matrix Models for Population, Disease, and Evolutionary Dynamics

English

2024

Life Sciences / Biology

Textbook

J. M. Cushing

Science

Student Mathematical Library

Trade Paperback

8.5 in

5.5 in

Scholarly & Professional

2023-050951

23/eng/20231212

106

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578.01/5129434

Population models Linear matrix models for structured populations Nonlinear matrix models for structured populations Disease and epidemic models Darwinian dynamics Appendices Bibliography Index

An introduction to the use of matrix theory and linear algebra in modeling the dynamics of biological populations. 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.)., 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.

QH323.5.C88 2024

4