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Analysis of a two prey one predator system with disease in the first prey population

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Abstract

In this paper we have developed an eco-epidemic model with two prey one predator population where only first prey population is infected by an infectious disease. The interaction between first prey and predator is assumed to be governed by a Holling type II functional response where the handling time of predator for second prey is also involved. A Lotka–Volterra functional response is taken to represent the interaction between second prey and predator. Next we have studied the positivity of the solutions of the system and analyzed the existence and stability of various equilibrium points. We have introduced a time delay in the model and discussed about the stability of delayed model. It is observed that the existence of stability switches occur around the interior equilibrium. Our important mathematical findings are also numerically verified using MATLAB. Finally eco-epidemiological implications of our analytical findings are addressed critically.

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Acknowledgments

The authors are very grateful to the anonymous referees and the Editor-in-Chief (Dr. Jian-Qiao Sun) 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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  1. Swarnali Sharma
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  2. G. P. Samanta
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Correspondence to G. P. Samanta.

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Sharma, S., Samanta, G.P. Analysis of a two prey one predator system with disease in the first prey population. Int. J. Dynam. Control 3, 210–224 (2015). https://doi.org/10.1007/s40435-014-0107-4

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