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Rabies is a major issue for human and animal health in the Arctic, yet little is known about its epidemiology. In particular, there is an ongoing debate regarding how Arctic rabies persists in its primary reservoir host, the Arctic fox (Vulpes lagopus), which exists in the ecosystem at very low population densities. To shed light on the mechanisms of rabies persistence in the Arctic, we built a susceptible-exposed-infectious-recovered (SEIR) epidemiological model of rabies virus transmission in an Arctic fox population interacting with red foxes (Vulpes vulpes), a rabies host that is increasingly present in the Arctic. The model suggests that rabies cannot be maintained in resource-poor areas of the Arctic, characterized by low Arctic fox density, even in the presence of continuous reintroduction of the virus by infected Arctic foxes from neighbouring regions. However, in populations of relatively high Arctic fox density, rabies persists under conditions of higher transmission rate, prolonged infectious period and for a broad range of incubation periods. Introducing the strong cyclical dynamics of Arctic prey availability makes simulated rabies outbreaks less regular but more intense, with an onset that does not neatly track peaks in Arctic fox density. Finally, interaction between Arctic and red foxes increases the frequency and/or the intensity of rabies outbreaks in the Arctic fox population. Our work suggests that disruption of prey cycles and increasing interactions between Arctic and red foxes due to climate change and northern development may significantly change the epidemiology of rabies across the Arctic.