A First Course in Mathematical Models of Population Growth (With MATLAB Programs)

Mathematical Biology is not as hierarchical and systematic as other areas of mathematics. However, one topic that is invariably included in any textbook on quantitative ecology is population dynamics. This book attempts to present in a systematic way the most common and elementary models of population growth. In this book the term population is used in a very general sense and hence the models can be applied to study the evolution of any type of biological organism. In each chapter the models are arranged in the order of mathematical complexity. The first chapter presents an overview of mathematical models and their characteristics. Chapter 2 discusses at length various discrete models of population growth. While chapter 3 discusses the classical deterministic models, chapter 4 includes extensions and recent modifications of the models presented in the previous chapter. The qualitative solutions of the models, which are sometimes more valuable and useful than quantitative solutions, are included in chapter 5. Properties of the logistic map, bifurcation diagrams, feigenbaum constant, an introduction to chaos and Lyapunov exponent are some of the topics covered in this chapter. Chapter 6 is devoted to classical models of interaction between two different species. Chapter 7 presents models on human and plant epidemiology. Finally, chapter 8 presents an introduction to stochastic models. The pre-requisites assumed are knowledge in difference equations, differential equations, matrix algebra and probability theory. A unique feature of the book is the inclusion of MATLAB M-files at the end of each chapter. These programs will definitely facilitate the reader to gain greater depth of knowledge about the models discussed in the respective chapter and obtain not only numerical solutions but also graphical understanding. The book can be prescribed for one semester course for postgraduate students or as an elective subject at advanced undergraduate level. The lucid presentation of the mathematical models interweaved with MATLAB programs would make this book an ideal one for the graduate and postgraduate students specializing in quantitative biology.