Epidemiological models for invasion and persistence of pathogens

Motivated by questions such as "Why do some diseases take off, while others die out?" and "How can we optimize the deployment of control methods," we introduce simple epidemiological concepts for the invasion and persistence of plant pathogens. An overarching modeling framework is then presented that can be used to analyze disease invasion and persistence at a range of scales from the microscopic to the regional. Criteria for invasion and persistence are introduced, initially for simple models of epidemics, and then for models with greater biological realism. Some ways in which epidemiological models are used to identify optimal strategies for the control of disease are discussed. Particular attention is given to the spatial structure of host populations and to the role of chance events in determining invasion and persistence of plant pathogens. Finally, three brief case studies are used to illustrate the practical applications of epidemiological theory to understand invasion and persistence of plant pathogens. These comprise long-term predictions for the persistence and control of Dutch elm disease; identification of methods to manage the spread of rhizomania on sugar beet in the U.K. by matching the scale of control with the spatial and temporal scales of the disease; and analysis of evolutionary change in virus control to identify risks of inadvertent selection for damaging virus strains.