Mathematical analysis of an eco-epidemiological predator–prey model with stage-structure and latency

被引：0
作者：
Lingshu Wang
Pei Yao
Guanghui Feng
机构：
[1] Hebei University of Economics and Business,School of Mathematics and Statistics
[2] Shijiazhuang Information Engineering Vocational College,Department of International Trade
[3] Shijiazhuang Mechanical Engineering College,Institute of Applied Mathematics
来源：
Journal of Applied Mathematics and Computing | 2018年 / 57卷
关键词：
Eco-epidemiological model; Stage structure; Latent period; Stability; Hopf bifurcation; 34K18; 34K20; 34K60; 92D25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, an eco-epidemiological predator–prey model with stage structure for the prey and a time delay describing the latent period of the disease is investigated. By analyzing corresponding characteristic equations, the local stability of the trivial equilibrium, the predator-extinction equilibrium, the disease-free equilibrium and the endemic equilibrium is addressed. The existence of Hopf bifurcations at the endemic equilibrium is established. By using Lyapunov functionals and LaSalle’s invariance principle, sufficient conditions are obtained for the global asymptotic stability of the trivial equilibrium, the predator-extinction equilibrium, the disease-free equilibrium and the endemic equilibrium of the model.
引用
收藏
页码：211 / 228
页数：17
相关论文
共 36 条
[1]  
Anderson RM(1978)Regulation and stability of host-parasite population interaction: I. Regulatory processes J. Anim. Ecol. 47 219-267
[2]  
May RM(2002)Geometric stability switch criteria in delay differential systems with delay dependent parameters SIAM J. Math. Anal. 33 1144-1165
[3]  
Beretta E(1999)A predator–prey model with disease in the prey Nonlinear Anal. 36 747-766
[4]  
Kuang Y(1979)Stability analysis for a vector disease model Rocky Mt. J. Math. 9 31-42
[5]  
Chattopadhyay J(2008)Complete global stability for an SIR epidemic model with delay-distributed or discrete Nonlinear Anal. Real World Appl. 11 55-59
[6]  
Arino O(2011)Stability and Hopf bifurcation analysis of an eco-epidemic model with a stage structure Nonlinear Anal. 74 1088-1106
[7]  
Cooke KL(2005)Stability and Hopf bifurcation of an eco-epidemiological model with delays Acta Math. Sci. 25A 57-66
[8]  
McCluskey C(2005)Analysis of eco-epidemiological SIS model with epidemic in the predator Chin. J. Eng. Math. 22 30-34
[9]  
Shi X(2002)Epidemics in predator–prey models: disease in the predators IMA J. Math. Appl. Med. Biol. 19 185-205
[10]  
Cui J(1997)Research on the suitable living environment of the Rana temporaria chensinensis larva, t Chinese J. Zool. 31 38-41
1234