Modeling with Compartments
by John A. Jacquez
This is a “how to” book on compartmental modeling. The interest in applying compartmental analysis prompted the writing of this more applied book on compartmental modeling. This book avoids the development of basic theory, to the extent possible, and concentrates on showing how to model various types of systems in a number of application areas. In one sense, this book is an extension of the more theoretical Compartmental Analysis in Biology and Medicine and the two are best used together.
The book is divided into two parts. In Part I the first three chapters cover: an introduction to compartmental modeling in Chapter 1, techniques used in modeling deterministic compartmental systems in Chapter 2, and stochastic compartmental systems in Chapter 3. Chapters 4 to 6 give basic material on identifiability, estimation of parameters and the design of experiments for deterministic compartmental systems from an applications oriented viewpoint. Part II, Chapters 7 to 10, gives examples of compartmental modeling for a number of different application areas. Models for epidemiology and population growth, spatial interactions, disease progression, pharmacokinetics and metabolic pathways are given in turn.
Focusing the presentation of identifiability and estimability on applications and ease of use has led to two new approaches. For practical purposes, identifiability can be checked with the use of estimation software. More importantly, the author defines a fundamental correlation matrix which gives the inherent correlations between parameters that are imposed by an experimental design. These correlations are not affected by the sampling errors. They are determined by the shape of the sum of squares surface around its minimum, when the sampling errors are zero, and that depends on the experimental design, i.e. the inputs, the things measured, i.e. the observation function(s), and the number and placement of samples. Thus the fundamental correlation matrix provides a new way of comparing experimental designs.
The software package SAAM II and STELLA are used, SAAM II for simulation and parameters estimation and STELLA for simulations.
Table of Contents
Part I. Compartmental Modeling
- Basics and Techniques for Modeling Deterministic Compartmental Systems
- Basics and Techniques for Modeling Stochastic Compartmental Systems
- Estimation and Estimability
- Design of Experiments
Part II. Applications
- Epidemiology and Population Growth
- Modeling Spatial / Geographic Effects
- Modeling Disease Progression with Stages
- Pharmacokinetics and Metabolic Pathways