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

作　　者：王丽敏[1] 雒志学[1] 王寿斌[1] 

机构地区：[1]兰州交通大学数理与软件工程学院,甘肃兰州730070

出　　处：《宁夏大学学报（自然科学版）》2015年第3期197-201,共5页Journal of Ningxia University(Natural Science Edition)

基　　金：国家自然科学基金项目资助(11061017)

摘　　要：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.

关 键 词：时滞 食饵-捕食 局部渐近稳定性 HOPF分支 

分 类 号：O175.12[理学—数学]