AI 中文总结
研究传染病对食物链的影响，通过在广义Lotka-Volterra方程支配的食物链模型中引入新参数实施SIR模型，发现传染病使捕食者种群规模有时振荡，顶级捕食者在特定参数下可能灭绝，且改变群落持久性。
AI 中文摘要
食物网已从生态和数学两方面得到广泛研究，但该领域多数模型未同时考虑传染病影响。本文研究并模拟了一个由猎物、捕食者和顶级捕食者构成的小型食物链，其受广义Lotka-Volterra方程支配，并在食物链中的一个物种上实施易感-感染-恢复（SIR）模型。为研究传染病对食物链的影响，引入新参数，改变感染物种的捕食和狩猎率。当传染病存在于捕食者中时，捕食者种群规模在某些情况下会振荡，顶级捕食者传染病存在时种群规模不振荡，但在特定参数范围内可能灭绝，且群落持久性对捕食者增加，对顶级捕食者降低。
英文摘要
Food webs have been extensively studied from both ecological and mathematical aspects. However, most of the models studied in this area do not capture the effects of infectious diseases simultaneously. Recently, the idea of including an infectious disease in a food web model has been investigated. We study and simulate a small food chain consisting of only prey, predators, and apex predators governed by the generalized Lotka-Volterra equations, and we implement the Susceptible-Infected-Recovered (SIR) model on only one of the species at a time in the food chain. To study the effects of an infectious disease on the food chain, we introduce a new parameter that increases the predation rate by a factor of $w$ and decreases the hunting rate by a factor of $1/w$ for infected species. When the infectious disease is present in predators, we observe that predators do not become extinct under any set of parameters; however, an oscillation in their population size occurs under some circumstances, which we do not observe in ordinary SIR or the generalized Lotka-Volterra equations alone. When an infectious disease is present in apex predators, oscillations in the population size do not happen; but if the set of parameters is in a specific range the apex predators may become extinct. Furthermore, the chance of survival of the community, known as community persistence, increases for the predators and decreases for the apex predators.
