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.
机构:
NE Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China
Changchun Univ, Sch Sci, Changchun 130022, Jilin, Peoples R ChinaNE Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China
Zhao, Yanan
;
Jiang, Daqing
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机构:
NE Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R ChinaNE Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China
机构:
School of Mathematics Science, Nanjing Normal University, Nanjing
Department of Mathematics, Xinyang Normal University, XinyangSchool of Mathematics Science, Nanjing Normal University, Nanjing
Zhou X.
;
Cui J.
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机构:
School of Mathematics Science, Nanjing Normal University, NanjingSchool of Mathematics Science, Nanjing Normal University, Nanjing
Cui J.
;
Shi X.
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机构:
Department of Mathematics, Xinyang Normal University, XinyangSchool of Mathematics Science, Nanjing Normal University, Nanjing
Shi X.
;
Song X.
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h-index: 0
机构:
Department of Mathematics, Xinyang Normal University, XinyangSchool of Mathematics Science, Nanjing Normal University, Nanjing
机构:
Xinyang Normal Univ, Coll Math & Informat Sci, Xinyang 464000, Henan, Peoples R ChinaXinyang Normal Univ, Coll Math & Informat Sci, Xinyang 464000, Henan, Peoples R China
Zhou, Xueyong
;
Shi, Xiangyun
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Xinyang Normal Univ, Coll Math & Informat Sci, Xinyang 464000, Henan, Peoples R ChinaXinyang Normal Univ, Coll Math & Informat Sci, Xinyang 464000, Henan, Peoples R China
Shi, Xiangyun
;
Song, Xinyu
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机构:
Xinyang Normal Univ, Coll Math & Informat Sci, Xinyang 464000, Henan, Peoples R ChinaXinyang Normal Univ, Coll Math & Informat Sci, Xinyang 464000, Henan, Peoples R China
机构:
NE Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China
Changchun Univ, Sch Sci, Changchun 130022, Jilin, Peoples R ChinaNE Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China
Zhao, Yanan
;
Jiang, Daqing
论文数: 0引用数: 0
h-index: 0
机构:
NE Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R ChinaNE Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China
机构:
School of Mathematics Science, Nanjing Normal University, Nanjing
Department of Mathematics, Xinyang Normal University, XinyangSchool of Mathematics Science, Nanjing Normal University, Nanjing
Zhou X.
;
Cui J.
论文数: 0引用数: 0
h-index: 0
机构:
School of Mathematics Science, Nanjing Normal University, NanjingSchool of Mathematics Science, Nanjing Normal University, Nanjing
Cui J.
;
Shi X.
论文数: 0引用数: 0
h-index: 0
机构:
Department of Mathematics, Xinyang Normal University, XinyangSchool of Mathematics Science, Nanjing Normal University, Nanjing
Shi X.
;
Song X.
论文数: 0引用数: 0
h-index: 0
机构:
Department of Mathematics, Xinyang Normal University, XinyangSchool of Mathematics Science, Nanjing Normal University, Nanjing
机构:
Xinyang Normal Univ, Coll Math & Informat Sci, Xinyang 464000, Henan, Peoples R ChinaXinyang Normal Univ, Coll Math & Informat Sci, Xinyang 464000, Henan, Peoples R China
Zhou, Xueyong
;
Shi, Xiangyun
论文数: 0引用数: 0
h-index: 0
机构:
Xinyang Normal Univ, Coll Math & Informat Sci, Xinyang 464000, Henan, Peoples R ChinaXinyang Normal Univ, Coll Math & Informat Sci, Xinyang 464000, Henan, Peoples R China
Shi, Xiangyun
;
Song, Xinyu
论文数: 0引用数: 0
h-index: 0
机构:
Xinyang Normal Univ, Coll Math & Informat Sci, Xinyang 464000, Henan, Peoples R ChinaXinyang Normal Univ, Coll Math & Informat Sci, Xinyang 464000, Henan, Peoples R China