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  • Title: Dynamics analysis of a predator-prey system with harvesting prey and disease in prey species.
    Author: Meng XY, Qin NN, Huo HF.
    Journal: J Biol Dyn; 2018 Dec; 12(1):342-374. PubMed ID: 29616595.
    Abstract:
    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.
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