TY  - GEN
AU  - Cushing, J.M.
TI  - Matrix models for population, disease and evolutionary dynamics
SN  - 9781470473341
U1  - 578.01 CUS 
PY  - 2024///
CY  - Providence
PB  - American Mathematical Society
KW  - Population Models
KW  - Epidemic Models
KW  - Darwinian Dynamics
KW  - Linear Matrix
KW  - Nonlinear Matrix
KW  - Biology
N1  - Include bibliography & index
N2  - 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 multivariable 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.

https://bookstore.ams.org/stml-106
ER  -