Abstract
The disease effect on ecological systems is an important issue from mathematical and experimental point of view. In this paper, we formulate and analyze a predator–prey model for the susceptible population, infected population and their predator population with modified Leslie–Gower (or Holling–Tanner) functional response. Mathematical analysis of the model equations with regard to invariance of nonnegativity and boundedness of solutions, local and global stability of the biological feasible equilibria and permanence of the system are presented. When the rate of infection crosses a critical value, we determine that the strictly positive interior equilibrium undergoes Hopf bifurcation. From our numerical simulations, we observe that the predation rate also plays an important role on the dynamic behavior of our system.
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This work is supported by the National Natural Science Foundation of China (No. 10771104 and No. 10771179) and Program for Innovative Research Team (in Science and Technology) in University of Henan Province.
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Zhou, X., Cui, J., Shi, X. et al. A modified Leslie–Gower predator–prey model with prey infection. J. Appl. Math. Comput. 33, 471–487 (2010). https://doi.org/10.1007/s12190-009-0298-6
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DOI: https://doi.org/10.1007/s12190-009-0298-6