title: 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.
authors.affiliation: Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK. A.M.Bate@bath.ac.uk
authors.forename: Andrew M
authors.initials: AM
authors.lastname: Bate
authors.forename: Frank M
authors.initials: FM
authors.lastname: Hilker
mesh_terms: D000820:Animal Diseases / Q000453:epidemiology* / Q000401:mortality; D000818:Animals; D050936:Basic Reproduction Number; D017753:Ecosystem; D019353:Endemic Diseases / Q000706:statistics & numerical data / Q000662:veterinary*; D020387:Food Chain; D054884:Host-Pathogen Interactions; D008954:Models, Biological; D011156:Population Density; D011157:Population Dynamics; D011235:Predatory Behavior / Q000502:physiology*