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A new non-autonomous model for migratory birds with Leslie–Gower Holling-type II schemes and saturation recovery rate

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  • Zhang, Yan
  • Chen, Shihua
  • Gao, Shujing
  • Fan, Kuangang
  • Wang, Qingyun

Abstract

Migratory birds are essential factors in the epidemiology of infectious diseases. This article discusses a new predator–prey model for susceptible migratory birds, infected migratory birds and predator species. Time-dependent coefficients are considered with the Leslie–Gower Holling-type II schemes and the saturated recovery rate in this new model. Some sufficient conditions for the extinction and permanence of diseases are established on the basis of relatively weak assumptions. The global attractiveness of the model is also given through spectral analysis and Liapunov function. Our results reveal that the infective species is extinct if the upper threshold value R∗≤1, whereas the model is permanent if the lower threshold value R∗>1. Numerical simulations are conducted to confirm the obtained results.

Suggested Citation

  • Zhang, Yan & Chen, Shihua & Gao, Shujing & Fan, Kuangang & Wang, Qingyun, 2017. "A new non-autonomous model for migratory birds with Leslie–Gower Holling-type II schemes and saturation recovery rate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 289-306.
    • Handle: RePEc:eee:matcom:v:132:y:2017:i:c:p:289-306
    DOI: 10.1016/j.matcom.2016.07.015
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    1. H. Chen & G. J. D. Smith & S. Y. Zhang & K. Qin & J. Wang & K. S. Li & R. G. Webster & J. S. M. Peiris & Y. Guan, 2005. "H5N1 virus outbreak in migratory waterfowl," Nature, Nature, vol. 436(7048), pages 191-192, July.
    2. Samrat Chatterjee & J. Chattopadhyay, 2007. "Role of migratory bird population in a simple eco-epidemiological model," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 13(1), pages 99-114, February.
    3. Sanders, Johnathan & Noble, Benjamin & Van Gorder, Robert A. & Riggs, Cortney, 2012. "Mobility matrix evolution for an SIS epidemic patch model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6256-6267.
    4. Zhao, Tingting & Xiao, Yanni, 2015. "Plant disease models with nonlinear impulsive cultural control strategies for vegetatively propagated plants," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 107(C), pages 61-91.
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