Temporal Analysis I Quantifying and Comparing Epidemics

A graphical plot of disease intensity (y) versus time (t) is known as a disease progress curve (DPC). For many purposes, this is the primary depiction of an epidemic, serving to summarize the interactions of host, pathogen, and the biological and physical environment on disease development. For convenience of expression, ‘epidemic’ and ‘disease progress curve’ often are used interchangeably in this book, although, in fact, the latter is merely a graphical summary of the former biological process. Although researchers have published disease progress curves throughout the 20th century, it was Vanderplank who made the most compelling case for the preparation and analysis of disease progress curves. Vanderplank’s concepts, originally proposed four decades ago, will be brought up several times. Although considerable advances have been made in recent years, it should be pointed out here that the ideas and approaches of Vanderplank still have a large influence on plant pathologists who are trying to understand epidemics. Researchers may have many (possibly overlapping) goals in characterizing a plant disease epidemic. At one level, a researcher may only be interested in determining if two or more epidemics are different (in some sense) from each other. In this situation, the population dynamics of disease are not of direct interest; rather, one is interested in which ‘treatments’ have higher (or lower) intensities of disease or rates of disease change. At another level, a researcher may be interested in quantifying how the environment, host, and pathogen affect disease dynamics for the explicit purpose of understanding the complex interactions that influence disease development. This understanding can be used, among other things: to predict disease intensity at a particular time; to quantify the effects of control strategies on epidemics; or ultimately, to develop a theoretical basis for determining whether or not an epidemic will occur, and in the event of occurrence, to identify factors affecting the magnitude of the rate of disease increase and the final intensity of disease.

Chapter topics include:

Introduction

General Concepts

How Does an Epidemic Occur?

Models

Control

Model Fitting

Comparing Disease Progress Curves

Models with Maximum Disease Intensity as a Parameter

Time-Varying Rate Term