Global stability and Hopf bifurcation of an eco-epidemiological model with time delay  

作　　者：Jinna Lu Xiaoguang Zhang Rui Xu 

机构地区：[1]School of Applied Mathematics Shanxi University of Finance and Economics Taiyuan 030006,Shanxi,P.R.China

出　　处：《International Journal of Biomathematics》2019年第6期1-21,共21页生物数学学报（英文版）

基　　金：the National Natural Science Foundation of China(Nos.11871316,11671241,11601294,11801340,11501340 and 11371368);the Natural Science Foundation of Shanxi Province(Nos.201801D221001,201801D121006,201801D221011,201601D021012 and 201801D221007);the Shanxi Scholarship Council of China under Grant No.2016-011;the Program for the Start-up of High-Level Talents of Shanxi University(No.232545029).

摘　　要：In this paper,an eco-epidemiological model with time delay representing the gestation period of the predator is investigated.In the model,it is assumed that the predator population suffers a transmissible disease and the infected predators may recover from the disease and become susceptible again.By analyzing corresponding characteristic equations,the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the disease-free and coexistence equilibria are established,respectively.By means of Lyapunov functionals and LaSalle’s invariance principle,sufficient condi tions are obtained for the global stability of the coexistence equilibrium,the disease-free equilibrium and the predator-extinct equilibrium of the system,respectively.

关 键 词：Eco-epidemiological model delay HOPF BIFURCATION LaSalle’s INVARIANCE principle global stability. 

分 类 号：O17[理学—数学]