Estimating the reproduction number, Rₒ, from individual-based models of tree disease spread

Tree populations worldwide are facing an unprecedented threat from a variety of tree diseases and invasive pests. Their spread, exacerbated by increasing globalisation and climate change, has an enormous environmental, economic and social impact. Computational individual-based models are a popular tool for describing and forecasting the spread of tree diseases due to their flexibility and ability to reveal collective behaviours. In this paper we present a versatile individual-based model with a Gaussian infectivity kernel to describe the spread of a generic tree disease through a synthetic treescape. We then explore several methods of calculating the basic reproduction number R0, a characteristic measurement of disease infectivity, defining the expected number of new infections resulting from one newly infected individual throughout their infectious period. It is a useful comparative summary parameter of a disease and can be used to explore the threshold dynamics of epidemics through mathematical models. We demonstrate several methods of estimating R0 through the individual-based model, including contact tracing, inferring the Kermack–McKendrick SIR model parameters using the linear noise approximation, and an analytical approximation. As an illustrative example, we then use the model and each of the methods to calculate estimates of R0 for the ash dieback epidemic in the UK.