Department of Mathematics and Statistics, University of Minnesota, Duluth, Minnesota 55812, USA.
Ecol Appl. 2011 Jun;21(4):1024-30. doi: 10.1890/10-1449.1.
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.
朊病毒可引起鹿和驼鹿等有蹄类动物的慢性消瘦病和其他可传播的海绵状脑病，它们在土壤中能保持多年的活性。有蹄类动物的繁殖年龄在朊病毒在土壤中的停留时间内。无病野生动物种群的繁殖和死亡受密度依赖机制的调节，这也是承载能力概念的基础。在这里，我们提出了一个易感鹿种群的模型，该模型具有密度依赖的种群调节、感染种群和感染易感动物的环境朊病毒库。当承载能力较低时，疾病不会持续存在。随着承载能力超过一个临界水平，慢性消瘦病就会侵袭易感种群并持续存在。在第二个更高的临界水平之上进一步增加承载能力，会产生稳定的极限环和动物种群与疾病之间的周期性流行。因此，该模型将 Rosenzweig 关于捕食者-猎物模型的丰度悖论扩展到了种群疾病模型中。随着朊病毒在土壤中的停留时间增加，达到临界承载能力的时间更早。增加承载能力的野生动物管理计划可能导致慢性消瘦病持续存在，甚至使动物种群不稳定，特别是在朊病毒存在多年的情况下。
