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Role of additional food in eco-epidemiological system with disease in the prey

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  • Sahoo, Banshidhar

Abstract

An eco-epidemiological system with disease in the prey incorporating additional food to predator is proposed. The main objective of this study is to show the role of additional food in an eco-epidemiological system. We analyze the proposed system by calculating two reproduction numbers. The dynamical behavior of the system is investigated from the point of view of stability and persistence both analytically and numerically. Using Pontryagin’s Maximum Principle, an optimal control problem is formulated and solved in presence of additional food to achieve the control of disease. Numerical results illustrate that there exists a critical infection rate above which disease free system can not be reached in absence of additional food. On the other hand suitable additional food has the capability to obtain a disease free system up to certain infection level. The system becomes disease free also in presence of seasonally varying infection rate providing suitable additional food to predator. This study introduces a new non-chemical method for controlling disease in eco-epidemiological system.

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  • Sahoo, Banshidhar, 2015. "Role of additional food in eco-epidemiological system with disease in the prey," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 61-79.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:61-79
    DOI: 10.1016/j.amc.2015.02.038
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    1. Dawei Zhao & Lianhai Wang & Shudong Li & Zhen Wang & Lin Wang & Bo Gao, 2014. "Immunization of Epidemics in Multiplex Networks," PLOS ONE, Public Library of Science, vol. 9(11), pages 1-5, November.
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    4. Fukuda, Eriko & Kokubo, Satoshi & Tanimoto, Jun & Wang, Zhen & Hagishima, Aya & Ikegaya, Naoki, 2014. "Risk assessment for infectious disease and its impact on voluntary vaccination behavior in social networks," Chaos, Solitons & Fractals, Elsevier, vol. 68(C), pages 1-9.
    5. Mukhopadhyay, B. & Bhattacharyya, R., 2009. "Role of predator switching in an eco-epidemiological model with disease in the prey," Ecological Modelling, Elsevier, vol. 220(7), pages 931-939.
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    Cited by:

    1. Agus Suryanto & Isnani Darti & Syaiful Anam, 2017. "Stability Analysis of a Fractional Order Modified Leslie-Gower Model with Additive Allee Effect," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2017, pages 1-9, May.
    2. Mbava, W. & Mugisha, J.Y.T. & Gonsalves, J.W., 2017. "Prey, predator and super-predator model with disease in the super-predator," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 92-114.
    3. Chakraborty, Bhaskar & Ghorai, Santu & Bairagi, Nandadulal, 2020. "Reaction-diffusion predator-prey-parasite system and spatiotemporal complexity," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    4. Ghosh, Joydev & Sahoo, Banshidhar & Poria, Swarup, 2017. "Prey-predator dynamics with prey refuge providing additional food to predator," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 110-119.

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