Postharvest diseases, especially those caused by fungi, can cause considerable damage to harvested apples in controlled atmosphere storage. Fungicides are used to control the disease, but resistance to fungicides is increasing and there is pressure by consumers and ecologists to reduce reliance on chemical controls. There is some evidence that physical conditions related to orchard management are predictive of postharvest disease incidence, and so the first line of defense against postharvest disease should involve best practices in orchards. In this work, we develop and analyse mathematical models to understand the dispersal of spores in the orchard, the initial infection level of fruit entering storage, and the epidemiology of the disease once the apples are in storage. We focus on conditions in the Okanagan Valley, where summers are dry and fungal spore presence is generally low. This leads to a mathematical problem where we are attempting to quantitatively and deterministically evaluate conditions surrounding rare events, that is, infection of fruit, and the fundamental stochasticity of the problem is crucial.