Impulsive modelling of rust dynamics and predator releases for biocontrol

Fungal diseases cause serious damages in crop worldwide. In particular, coffee leaf rust (CLR), caused by fungus Hemileia vastatrix attacks coffee leaves and reduces coffee yield. This paper presents a multi-seasonal model of the CLR development in the coffee plantation with continuous dynamics during the rainy season and a discrete event to represent the simpler dynamics during the dry season. Biological control using predators through one or more discrete introduction events over the year is then added. Analytical and semi-numerical studies are performed to identify how much and how frequently predators need to be introduced through the definition of a threshold value, as a function of various parameters. We show that the best strategy to efficiently control the disease depends on the predator mortality: low mortality parasites need be released only once a year, while high mortality parasites should be released more frequently to ensure their persistence in the plantation. This work hence provides qualitative and quantitative bases for the deployment of predator-based biocontrol, a promising alternative to fungicides for rust control.