Cost-Effective Control of Plant Disease When Epidemiological Knowledge Is Incomplete: Modelling Bahia Bark Scaling of Citrus

A spatially-explicit, stochastic model is developed for Bahia bark scaling, a threat to citrus production in north-eastern Brazil, and is used to assess epidemiological principles underlying the cost-effectiveness of disease control strategies. The model is fitted via Markov chain Monte Carlo with data augmentation to snapshots of disease spread derived from a previously-reported multi-year experiment. Goodness-of-fit tests strongly supported the fit of the model, even though the detailed etiology of the disease is unknown and was not explicitly included in the model. Key epidemiological parameters including the infection rate, incubation period and scale of dispersal are estimated from the spread data. This allows us to scale-up the experimental results to predict the effect of the level of initial inoculum on disease progression in a typically-sized citrus grove. The efficacies of two cultural control measures are assessed: altering the spacing of host plants, and roguing symptomatic trees. Reducing planting density can slow disease spread significantly if the distance between hosts is sufficiently large. However, low density groves have fewer plants per hectare. The optimum density of productive plants is therefore recovered at an intermediate host spacing. Roguing, even when detection of symptomatic plants is imperfect, can lead to very effective control. However, scouting for disease symptoms incurs a cost. We use the model to balance the cost of scouting against the number of plants lost to disease, and show how to determine a roguing schedule that optimises profit. The trade-offs underlying the two optima we identify—the optimal host spacing and the optimal roguing schedule—are applicable to many pathosystems. Our work demonstrates how a carefully parameterised mathematical model can be used to find these optima. It also illustrates how mathematical models can be used in even this most challenging of situations in which the underlying epidemiology is ill-understood.Author Summary: We consider how mathematical models can be used to inform the control of plant disease, even when the identity and biology of the pathogen are not well understood. This is often the case: control of emerging epidemics is most likely to have a significant effect when epidemics remain small, but little may then be known. We analyse data from an experimental plot concerning spread of Bahia bark scaling of citrus, an economically-important disease in north-eastern Brazil, by fitting a mathematical model, which also accounts for uncertainty, to disease spread. Our model captures the epidemiological features of the disease, revealing that transmission is localised and that disease spreads relatively slowly. We use the model to investigate fundamental trade-offs underlying cultural disease control at scales relevant to citrus production. We show how optimal planting densities can be defined, which balance slower spread of disease against the profit that would be lost by growing fewer plants. We also show how the cost of looking for and removing symptomatically diseased plants can be balanced against the reduced disease it leads to. Ours is the first study to consider how a parameterised mathematical model can be used to design optimised cultural controls of plant disease.