Temporal Analysis III Advanced Topics

In this chapter we consider additional complexities of epidemics that are important in some circumstances. We introduce crop growth into the models. We will introduce two main categories of crop growth scenarios. This serves as an introduction to the many possible types of disease dynamics that can occur when the host population “size” changes. Then, we consider in more detail the primary infections that initiate an epidemic. We will discuss how disease dynamics change when these primary infections occur over the duration of the epidemic rather than just at the start. A special case of the model is the one for a monocyclic disease. We will then use the insight gained from the previous sections to study plant diseases caused by viruses. In particular, we deal with the situation in which the pathogen is transmitted from infected plants to healthy plants by the feeding activity of vectors, usually herbivorous insect species (such as aphids and leafhoppers). We will study the consequences of vectored transmission on the development of epidemics, and use this system to demonstrate how such models can be utilized to evaluate disease control strategies. We will discuss situations where insight into epidemics depends on more than the use of mathematical analysis, and results are obtainable only by the use of computer programs. Finally, we conclude the chapter by discussing ways of fitting some of the differential-equation models directly (or indirectly) to data.

Chapter topics include:

Introduction

Models with Crop Growth

The Role of Primary Infection

Epidemics with Vector Transmission

Transitional Dynamics and Other Complexities

Parameter Estimation