Hsieh Ying-Hen, Hsiao Chin-Kuei
Department of Public Health and Biostatistics Center, China Medical University, 91 Hsueh-Shih Road, Taichung, Taiwan 404.
Math Med Biol. 2008 Sep;25(3):247-66. doi: 10.1093/imammb/dqn017. Epub 2008 Aug 12.
A predator-prey model with disease infection in both populations is proposed to account for the possibility of a contagious disease crossing species barrier from prey to predator. We obtain several threshold parameters from local analysis of various equilibria of the proposed system as well as coupled conditions on these threshold parameters which determine the stability of these equilibria. One of the coupled conditions, in the form of an ecological threshold number for the predator-prey ecosystem, always determines the coexistence of predators and prey. The other condition, in the form of a disease basic reproduction number, dictates whether the disease will become endemic in the ecosystem. Under one combination of these coupled conditions, a highly infectious disease could drive the predators to extinction when predators and prey would have coexisted without the disease. For another combination of the conditions, the predation of the more vulnerable infected prey could cause the disease to be eradicated in the ecosystem, in some case even approaching a disease-free periodic solution, when the disease would have otherwise remained endemic in the prey population in the absence of predation. This indicates that the presence of disease in both predators and prey could either promote or impair coexistence, and its precise impact needs to be explored specifically in each particular situation. By considering disease infection in both populations, our model also yields more complex dynamics, allowing for the possibility of bistability and periodic oscillation, in either disease-free or endemic states, in the ecosystem for which the conditions are obtained analytically and with the help of numerical simulations.
提出了一个在两个种群中都存在疾病感染的捕食者 - 猎物模型，以解释传染病跨越物种屏障从猎物传播到捕食者的可能性。我们从所提出系统的各种平衡点的局部分析中获得了几个阈值参数，以及这些阈值参数上的耦合条件，这些条件决定了这些平衡点的稳定性。其中一个耦合条件，以捕食者 - 猎物生态系统的生态阈值数的形式，总是决定捕食者和猎物的共存。另一个条件，以疾病基本繁殖数的形式，决定疾病是否会在生态系统中成为地方病。在这些耦合条件的一种组合下，当没有疾病时捕食者和猎物本可以共存的情况下，一种高传染性疾病可能会导致捕食者灭绝。对于条件的另一种组合，捕食更易感染的猎物可能会导致疾病在生态系统中被根除，在某些情况下甚至接近无病周期解，而在没有捕食的情况下，疾病原本会在猎物种群中保持地方病状态。这表明捕食者和猎物中都存在疾病既可能促进也可能损害共存，其确切影响需要在每个特定情况下具体探索。通过考虑两个种群中的疾病感染，我们的模型还产生了更复杂的动态，在无病或地方病状态下，在生态系统中允许出现双稳态和周期性振荡的可能性，为此通过解析和借助数值模拟获得了条件。
