一类具有时滞且疾病在捕食者中传播的生态传染病模型分析

Analysis of An Ecological Epidemic Model with Time Delay and Disease Spreads in Predator

通过假设捕食者与食饵均为密度制约的、疾病在捕食者中传播、染病捕食者不具备捕食和生育能力,且染病者不能恢复,建立了一类食饵-捕食系统的SI传染病模型,并引入了疾病潜伏期时滞τ(τ≥0),利用特征根法和Routh-Hurwitz判据分析了系统各个平衡点的局部渐近稳定性以及平衡点处Hopf分支的存在性.

An SI epidemic model of prey-predator is established by assuming that the prey and predator are both density dependent,the disease spreads in predator,the infected predator can＇t prey,procreate or recover.The incubation periodτof the disease is also taken into account.Then the system＇s local asymptotic stability at every equilibrium point and the Hopf＇s existences of the equilibrium points are analyzed by using the characteristic root method and Routh-Hurwith criterion.