Mathematical Models in Population Biology and Epidemiology

Mathematical Models in Population Biology and Epidemiology

2012 | Fred Brauer • Carlos Castillo-Chavez
The second edition of "Mathematical Models in Population Biology and Epidemiology" was written to update and expand the first edition, which had already become a significant resource for the computational, mathematical, modeling, and theoretical biology communities. The field of population biology has grown substantially, making it necessary to revise the book to reflect current research and include new topics. The core of the first edition was retained, with corrections to errors and an addition of a new chapter on spatiotemporal dynamics of populations. The chapters on disease dynamics and control were expanded, and a new chapter on spatially structured populations was introduced. The book also includes more exercises and projects focused on biology. The book is intended to inspire students in the biological sciences to incorporate mathematics into their scientific approach. It aims to demonstrate the genuine use of mathematics in biology by describing models in population biology and the mathematics used to analyze them, along with case studies. A secondary goal is to expose mathematics students to the modeling process in the natural and social sciences. The book assumes a year of calculus, some background in elementary differential equations, and a little matrix theory. The mathematical treatment focuses on approximate and qualitative methods rather than explicit solutions. The book includes a new chapter on spatiotemporal dynamics of populations, and additional exercises and projects. It also includes a chapter on spatially structured populations, introducing diffusion, reaction-diffusion, and metapopulation modeling frameworks. The book also includes a chapter on disease transmission models, covering epidemic models, endemic diseases, and parameter estimation. The book is structured into four parts: simple single-species models, models for interacting species, structured population models, and disease transmission models. The book includes a prologue on population dynamics, discussing the challenges of predicting population growth and the role of mathematical models in understanding these dynamics. The book also includes a bibliography and index. The book is intended to be an introduction to the principles and practice of mathematical modeling in the biological sciences, and it is not the last word on the subject.The second edition of "Mathematical Models in Population Biology and Epidemiology" was written to update and expand the first edition, which had already become a significant resource for the computational, mathematical, modeling, and theoretical biology communities. The field of population biology has grown substantially, making it necessary to revise the book to reflect current research and include new topics. The core of the first edition was retained, with corrections to errors and an addition of a new chapter on spatiotemporal dynamics of populations. The chapters on disease dynamics and control were expanded, and a new chapter on spatially structured populations was introduced. The book also includes more exercises and projects focused on biology. The book is intended to inspire students in the biological sciences to incorporate mathematics into their scientific approach. It aims to demonstrate the genuine use of mathematics in biology by describing models in population biology and the mathematics used to analyze them, along with case studies. A secondary goal is to expose mathematics students to the modeling process in the natural and social sciences. The book assumes a year of calculus, some background in elementary differential equations, and a little matrix theory. The mathematical treatment focuses on approximate and qualitative methods rather than explicit solutions. The book includes a new chapter on spatiotemporal dynamics of populations, and additional exercises and projects. It also includes a chapter on spatially structured populations, introducing diffusion, reaction-diffusion, and metapopulation modeling frameworks. The book also includes a chapter on disease transmission models, covering epidemic models, endemic diseases, and parameter estimation. The book is structured into four parts: simple single-species models, models for interacting species, structured population models, and disease transmission models. The book includes a prologue on population dynamics, discussing the challenges of predicting population growth and the role of mathematical models in understanding these dynamics. The book also includes a bibliography and index. The book is intended to be an introduction to the principles and practice of mathematical modeling in the biological sciences, and it is not the last word on the subject.
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