Abstract

Global food security concerns are likely to remain prominent as population growth and climate change increase pressures on food production. With commonly-used techniques for controlling crop diseases, such as fungicides and crop rotation, subject to ecological, economic and environmental disadvantages, experimentalists have become increasingly interested in biological control, where a natural enemy of a pathogen is deployed to reduce disease. We initially consider the probability of invasion in the stochastic SIS epidemiological model, focussing on the case where the population size is relatively small. We demonstrate analytically how the probability of an epidemic occurring depends sensitively on the exact definition used to define an epidemic, and how the response is affected by both the population size and the basic reproductive number of the pathogen. Our analysis is then extended to deterministic and stochastic adaptations of the SIS model where an agent of biological control is incorporated. In particular, we determine conditions for biological control to be able to eradicate a particular pathogen, and how eradication is conditioned on the epidemiology of the underlying host-pathogen interaction as well as the level and timing of application. Our results have clear significance in terms of optimising the deployment of biological control and explaining the variability that has all too often beset performance in the field.