Predator-prey oscillations can shift when diseases become endemic

Andrew Bate, Frank Hilker

Research output: Contribution to journalArticlepeer-review

22 Citations (SciVal)


In epidemiology, knowing when a disease is endemic is important. This is usually done by finding the basic reproductive number, R0, 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 View the MathML source is what determines whether a disease is endemic, and not on the equilibrium-based basic reproductive number View the MathML source. These findings undermine any R0 analysis based solely on steady states when predator–prey oscillations exist for density dependent diseases.
Original languageEnglish
Pages (from-to)1-8
JournalJournal of Theoretical Biology
Publication statusPublished - 7 Jan 2013


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