Biological invasions can have negative consequences for resident biota, particularly when disease-causing organisms are involved. Austropuccinia psidii, or guava rust, has rapidly spread through the tropics affecting both native and non-native Myrtaceae. In Puerto Rico, the rust has become common on Syzygium jambos, an invasive tree native to South-East Asia. What are the drivers of infection, and do refugia exist across a heterogeneous landscape? We address these questions using species distribution modelling and beta regressions. The realized and potential distribution of Syzygium jambos is extensive. The model produced an AUC of 0.88, with land-use categories and precipitation accounting for 61.1% of the variation. Predictability of S. jambos is highest in disturbed habitats, especially in mountainous regions with high precipitation. All 101 trees surveyed and measured across Puerto Rico showed signs of infection to varying extents. Infection severity was consistently associated with annual mean temperature in all top beta regression models, but was also commonly associated with tree size and precipitation variables. We found no safe sites for S. jambos. Many trees were extremely unhealthy and some were dead, suggesting that S. jambos may soon become extinct on the island or reduced to persistent stump sprouts. Native vegetation may benefit from the local demise of S. jambos. While the rust has not jumped to native Myrtaceae, vigilance is required, as host-shifts have occurred in other tropical regions.