Dynamics analysis of a predator-prey system with harvesting prey and disease in prey species

被引:63
作者
Meng, Xin-You [1 ]
Qin, Ni-Ni [1 ]
Huo, Hai-Feng [1 ]
机构
[1] Lanzhou Univ Technol, Sch Sci, Lanzhou, Gansu, Peoples R China
基金
中国国家自然科学基金;
关键词
Predator-prey; time delay; Hopf bifurcation; optimal harvesting policy; BIFURCATION-ANALYSIS; EPIDEMIC MODEL; STABILITY; POPULATION; MANAGEMENT; THRESHOLD; EQUATIONS; INFECTION; DISCRETE; DELAYS;
D O I
10.1080/17513758.2018.1454515
中图分类号
Q14 [生态学(生物生态学)];
学科分类号
071012 ; 0713 ;
摘要
In this paper, a predator-prey system with harvesting prey and disease in prey species is given. In the absence of time delay, the existence and stability of all equilibria are investigated. In the presence of time delay, some sufficient conditions of the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analysing the corresponding characteristic equation, and the properties of Hopf bifurcation are given by using the normal form theory and centre manifold theorem. Furthermore, an optimal harvesting policy is investigated by applying the Pontryagin's Maximum Principle. Numerical simulations are performed to support our analytic results.
引用
收藏
页码:342 / 374
页数:33
相关论文
共 45 条
[41]   Optimal treatment of an SIR epidemic model with time delay [J].
Zaman, Gul ;
Kang, Yong Han ;
Jung, Il Hyo .
BIOSYSTEMS, 2009, 98 (01) :43-50
[42]  
[张江山 Zhang Jiangshan], 2005, [生物数学学报, Journal of Biomathematics], V20, P157
[43]   The threshold of a stochastic SIRS epidemic model with saturated incidence [J].
Zhao, Yanan ;
Jiang, Daqing .
APPLIED MATHEMATICS LETTERS, 2014, 34 :90-93
[44]   A modified Leslie-Gower predator-prey model with prey infection [J].
Zhou X. ;
Cui J. ;
Shi X. ;
Song X. .
Journal of Applied Mathematics and Computing, 2010, 33 (1-2) :471-487
[45]   ANALYSIS OF A DELAY PREY-PREDATOR MODEL WITH DISEASE IN THE PREY SPECIES ONLY [J].
Zhou, Xueyong ;
Shi, Xiangyun ;
Song, Xinyu .
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2009, 46 (04) :713-731