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Dynamical Behaviour of an Epidemic Model with Disease in Top-Predator Population Only: A Bifurcation Study

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Abstract

In ecology, disease in the top-predator population plays an important role for controlling chaotic dynamics of a predator-prey system. We modify Hastings and Powell’s (HP) (Hastings and Powell, Ecology 72:896–903, 1991) food chain model by introducing disease in the top-predator population only. The modified model is analysed to obtain different conditions for which the system exhibits stability around the biologically feasible equilibrium points. Through numerical simulations we display that the modified system enters into periodic solutions depending upon the force of infection and half saturation constant. In addition, we study numerically that the system undergoes a saddle-node bifurcation. We utilize the MATCONT2.5.1 package to obtain various kinds of Hopf points and their continuation curves in the proposed model. Our results demonstrate that infection rate of top-predator population is the key parameter for controlling the chaotic dynamics observed in original HP model.

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Acknowledgments

The author is extremely thankful to the anonymous honourable reviewers for their critical comments and valuable suggestions which have immensely improved the content in this version.

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  1. Department of Applied Mathematics, University of Calcutta, Kolkata, West Bengal, India

    Banshidhar Sahoo

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Sahoo, B. Dynamical Behaviour of an Epidemic Model with Disease in Top-Predator Population Only: A Bifurcation Study. Differ Equ Dyn Syst 28, 153–176 (2020). https://doi.org/10.1007/s12591-016-0307-9

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