Moyé A.L., Kapadia S.A. Difference equations with public health applications

New York: Marcel Dekker, Inc., 2000. — 392 p. — (Biostatistics; vol. 6). — ISBN: 0-8247-0447-9.The book is a new contribution to didactic textbooks in mathematics, offering a contemporary introduction and exploration of difference equations in public health. The text begins with an elementary discussion of difference equations with definitions of the basic types of equations. Since intuition is best built incrementally, development of the solution of these equations begins with the simplest equations, moving on to the more complicated solutions of more complex equations. In addition, many examples for the complete solutions of families of difference equations in their complete detail are offered. The solution methods of induction and of partial fractions are discussed and provided. Solutions from partial fractions are contrasted to other forms of the solution in terms of the effort in obtaining the solution (identification and the relative comprehensive ease of the solutions). Expansive exercises are provided at the end of each chapter.
Chapter 1 provides a general introduction to the difference equation concept, establishes notation, and develops the iterative solution useful for firstorder equations. Chapters 2 and 3 discuss the generating function concept and develop the tools necessary to successfully implement this approach. Chapter 4 combines the results of the first three chapters, demonstrating through discussion and numerous examples, the utility of the generating function approach in solving homogeneous and nonhomogenous difference equations. Chapter 5 addresses the complicated topic of difference equations with variable coefficients. Chapter 6 introduces a collection of difference equation systems developed by the authors which are useful in public health research. Chapters 7-10 applies these systems to problems in public health. Finally, the application of difference equations to epidemiologic models is provided through the treatment of immigration, birth, death, and emigration models in Chapters 11 and 12. Solutions for combinations of these models are also provided.
Students in undergraduate or graduate programs in statistics, biostatistics, operations research, stochastic processes, and epidemiology compose the target audience for this book, as well as researchers whose work involves solutions to difference equations. It is envisioned that this book will be the foundation text for a course on difference equations in biostatistics, mathematics, engineering, and statistics.