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Bifurcation and control of an eco-epidemiological system with environmental fluctuations: a stochastic approach

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Abstract

This paper describes the dynamics of an infectious disease transmission modified Leslie–Gower type eco-epidemiological system in both deterministic and stochastic fluctuating environments with harvesting. The dynamics of the deterministic system is extensively investigated around coexistence equilibria. Sufficient conditions are derived for local and global stability of the system. The existence of Hopf bifurcation phenomenon is examined around interior equilibria of the system. Subsequently, we use normal form method and center manifold theorem to examine the nature of the Hopf bifurcation. The obtained results are useful to extract the criteria for disease extinction and control perspective. Later, a white noise term is incorporated to the system to describe the dynamics of the system in stochastic fluctuating environment. Sufficient conditions are derived for the mean square stability (MSS) of the system which can be used to evaluate necessary conditions for the asymptotic MSS and a threshold condition between asymptotic MSS and unstable system. Finally, some numerical simulations are carried out, and graphical illustrations are given in support of the analytical results obtained in both deterministic and stochastic systems.

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Acknowledgments

Mr. Haldar is very much thankful to UGC (ERO) for the fellowship under FDP scheme of UGC vide Letter No. F.TF.WB-009-01/13-14(ERO) dated 11.07.2013.

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Authors and Affiliations

  1. Department of Mathematics, Hooghly Womens’ College, Pipulpati, Hooghly, 712103, West Bengal, India

    Samadyuti Haldar

  2. Information Services and Ocean Sciences Group, Indian National Centre for Ocean Information Services, Hyderabad, “Ocean Valley”, Pragathi Nagar(BO), Nizampet(SO), Hyderabad, 500090, India

    Kunal Chakraborty

  3. Department of Mathematics, Sashinara High School, Sashinara, Memari, Burdwan, 713146, India

    Kunal Das

  4. Department of Mathematics, Indian institute of Engineering Science and Technology, Shibpur, Howrah, 711103, India

    T. K. Kar

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  1. Samadyuti Haldar
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Correspondence to Samadyuti Haldar.

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Haldar, S., Chakraborty, K., Das, K. et al. Bifurcation and control of an eco-epidemiological system with environmental fluctuations: a stochastic approach. Nonlinear Dyn 80, 1187–1207 (2015). https://doi.org/10.1007/s11071-015-1935-2

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