Stable limit cycles and the paradox of enrichment in a model of chronic wasting disease

Prions, which cause chronic wasting disease and other transmissible spongiform encephalopathies in ungulates, can remain active in soils for years. The reproductive age of ungulate populations is well within the residence time of prions in the soil. Reproduction and mortality in disease-free wildlife populations is regulated by density-dependent mechanisms, which also underlie the concept of carrying capacity. Here, we present a model of a susceptible deer population with density-dependent population regulation, an infected population, and an environmental pool of prions that infect the susceptible animals. When carrying capacity is low, the disease does not persist. As carrying capacity increases beyond a critical level, chronic wasting disease then invades a susceptible population and persists. Further increases in carrying capacity beyond a second, higher critical level produce stable limit cycles and recurrent epidemics between the animal population and the disease. This model therefore extends Rosenzweig's paradox of enrichment for predator-prey models to models of diseases in populations. The critical carrying capacities are reached sooner as the residence time of the prion in the soil increases. Wildlife management programs which increase carrying capacity may cause chronic wasting disease to persist and even destabilize animal populations, especially where prions persist for many years.