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A ratio-dependent predator-prey model with Allee effect and disease in prey

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Abstract

In this paper, we have developed a ratio-dependent predator-prey model with disease in prey. The total population is subdivided into three sub-classes, namely susceptible prey, infected prey and predator population. A susceptible prey survival threshold has been incorporated for Allee effect in the model. We have studied the positivity and boundedness of the solutions of the system and analyzed the existence of various equilibrium points and stability of the system at those equilibrium points for both strong and weak Allee effect. It is observed that a Hopf bifurcation may occur about the interior equilibrium taking susceptible prey survival threshold for Allee effect as bifurcation parameter. Our analytical findings are illustrated through computer simulation using MATLAB, which show the reliability of our model from the eco-epidemiological point of view.

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Acknowledgments

The authors are very grateful to the anonymous referees and the Editor-in-Chief (Chin-Hong Park, Ph.D) for their careful reading, valuable comments and helpful suggestions, which have helped them to improve the presentation of this work significantly.

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  1. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, 711 103, India

    Swarnali Sharma & G. P. Samanta

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Sharma, S., Samanta, G.P. A ratio-dependent predator-prey model with Allee effect and disease in prey. J. Appl. Math. Comput. 47, 345–364 (2015). https://doi.org/10.1007/s12190-014-0779-0

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