Predator-prey oscillations can shift when diseases become endemic

Abstract In epidemiology, knowing when a disease is endemic is important. This is usually done by finding the basic reproductive number, R 0 , using equilibrium-based calculations. However, oscillatory dynamics are common in nature. Here, we model a disease with density dependent transmission in an oscillating predator–prey system. The condition for disease persistence in predator–prey cycles is based on the time-average density of the host and not the equilibrium density. Consequently, the time-averaged basic reproductive number R 0 ¯ is what determines whether a disease is endemic, and not on the equilibrium-based basic reproductive number R 0 ⁎ . These findings undermine any R 0 analysis based solely on steady states when predator–prey oscillations exist for density dependent diseases.