An introduction to mathematical modeling of infectious diseases
This book is a unique contribution to Springer's Mathematics of Planet Earth series, in which I have indulged myself for the past few weeks. It is suitable for upper undergraduate and beginning graduate students who are interested in mathematical modeling of epidemics. Although the book is written in a concise manner, the details of the proofs are reasonably elaborated and specific references are provided for the reader. The book consists of five chapters. In the first introductory chapter, essential elements such as basic reproduction number, incidence rates, latency, immunity, demography, route of transmission, vaccination and quarantine are detailed. Chapter 2 deals with five epidemic models and their analysis including the Kermack-McKerndrick model, a model for diseases with no immunity, a model with demography, a homogeneous SIR model, and Ross-MacDonald model. Chapter 3 is the main part of the book which provides some necessary mathematical tools and techniques. These include stability analysis of equilibrium solutions, linearization, Lyapunov functions, periodic solutions, phase-line analysis and monotone systems. Chapter 4 introduces parameter estimation as well as nonlinear least squares methods. A couple of special topics on SEIR models and in-host models are briefly discussed in the last chapter.
scientific article; zbMATH DE number 6823412