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An eco-epidemic pest-natural enemy SI model in two patchy habitat with impulsive effect

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Abstract

In this paper, the dynamics of a pest-natural enemy model with impulsive diffusion of pest in two patchy habitat is studied by considering the disease in pest population with two classes: susceptible, infectious and the disease is transmitted from infected pest to susceptible pest and does not propagate to the natural enemy. To reduce the pest at a desired level, the infected pest and natural enemy are impulsively released in both the patches. In the analysis, it is obtained that the susceptible pest free periodic solution is locally asymptotically stable by exploiting the Floquet theory of impulsive differential equation and small amplitude perturbation skills. It is also globally asymptotically stable using comparison techniques of impulsive differential equations. The study shows that the infection incidence rates and impulsive techniques play an important role on the dynamics of pest control system. Moreover, a short impulse period and large releasing amount of infected pest and natural enemy are cause the extinction of pest population. Finally, numerical simulations are carried out to validate our theoretical findings.

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Acknowledgments

This work is supported by the University Grant Commission, New Delhi (No. F.30-56/2014(BSR)).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Dr. Harisingh Gour Central University, Sagar, Madhya Pradesh, India

    Kunwer Singh Mathur

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  1. Kunwer Singh Mathur
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Correspondence to Kunwer Singh Mathur.

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Mathur, K.S. An eco-epidemic pest-natural enemy SI model in two patchy habitat with impulsive effect. Int. J. Appl. Comput. Math 3, 2671–2685 (2017). https://doi.org/10.1007/s40819-016-0209-0

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  • DOI: https://doi.org/10.1007/s40819-016-0209-0

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