Mathematical models in population biology and epidemiology.

*(English)*Zbl 0967.92015
Texts in Applied Mathematics. 40. New York, NY: Springer. xxiii, 416 p. (2001).

The eminent researchers introduce principles and practice of mathematical modelling in biological sciences. They discuss models that arise in population biology, epidemiology and resource management, and the mathematics useful in analysing them. The book consists of eight chapters divided into three parts.

Part I focuses on the description and analysis of single species models including those commonly used to predict the growth of human and animal populations together with their usefulness and limitations. Chapter 1 deals with continuous-time models, like logistic and harvesting populations. Chapter 2 discusses discrete systems with non-overlapping generations. Impact on biological growth rates is not always instantaneous. The use of distributed delays leads to the study of differential-difference equation models, which is the topic of Chapter 3.

Part II of this book looks at mechanisms that drive multiserver interactions such as competition, mutualism and predator-prey interactions. Conditions for species coexistence or competetive exclusion are established. Chapter 4 considers populations with two age classes and Chapter 5 discusses age in various implicit forms. Chapter 6 discusses harvesting in two-species models with economic aspects.

Part III describes population structure in two separate ways. Chapter 7 classifies individuals according to their epidemiological status. Chapter 8 incorporates age structure in the Malthus model leading to the prototypes of age structured models. This part also presents mathematical challenges faced in the field of structured populations. The book also illustrates the usefulness of the models through case studies representing real-life situations.

The emphasis of the book is on describing the mathematical results and showing students how to apply them. A large number and variety of examples, exercises and projects are included. The treatment is not only more appropriate for understanding, but even more effective. The work provides an easily accessible, but concise introduction to the subject. Both graduate students and professionals will find the book an understandable, absorbing and penetrating treatment of a beautiful theory.

Part I focuses on the description and analysis of single species models including those commonly used to predict the growth of human and animal populations together with their usefulness and limitations. Chapter 1 deals with continuous-time models, like logistic and harvesting populations. Chapter 2 discusses discrete systems with non-overlapping generations. Impact on biological growth rates is not always instantaneous. The use of distributed delays leads to the study of differential-difference equation models, which is the topic of Chapter 3.

Part II of this book looks at mechanisms that drive multiserver interactions such as competition, mutualism and predator-prey interactions. Conditions for species coexistence or competetive exclusion are established. Chapter 4 considers populations with two age classes and Chapter 5 discusses age in various implicit forms. Chapter 6 discusses harvesting in two-species models with economic aspects.

Part III describes population structure in two separate ways. Chapter 7 classifies individuals according to their epidemiological status. Chapter 8 incorporates age structure in the Malthus model leading to the prototypes of age structured models. This part also presents mathematical challenges faced in the field of structured populations. The book also illustrates the usefulness of the models through case studies representing real-life situations.

The emphasis of the book is on describing the mathematical results and showing students how to apply them. A large number and variety of examples, exercises and projects are included. The treatment is not only more appropriate for understanding, but even more effective. The work provides an easily accessible, but concise introduction to the subject. Both graduate students and professionals will find the book an understandable, absorbing and penetrating treatment of a beautiful theory.

Reviewer: P.R.Parthasarathy (Chennai)