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

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang, 050061, People’s Republic of China

    Lingshu Wang

  2. Department of International Trade, Shijiazhuang Information Engineering Vocational College, Shijiazhuang, 050035, People’s Republic of China

    Pei Yao

  3. Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang, 050003, People’s Republic of China

    Guanghui Feng

Authors
  1. Lingshu Wang
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  2. Pei Yao
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  3. Guanghui Feng
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Corresponding author

Correspondence to Lingshu Wang.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 11371368), the Scientific Research Foundation of Hebei Education Department (No. QN2014040) and the Foundation of Hebei University of Economics and Business (No. 2015KYQ01).

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Wang, L., Yao, P. & Feng, G. Mathematical analysis of an eco-epidemiological predator–prey model with stage-structure and latency. J. Appl. Math. Comput. 57, 211–228 (2018). https://doi.org/10.1007/s12190-017-1102-7

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  • DOI: https://doi.org/10.1007/s12190-017-1102-7

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