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Effects of allochthonous inputs in the control of infectious disease of prey

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  • Sahoo, Banshidhar
  • Poria, Swarup

Abstract

Allochthonous inputs are important sources of productivity in many food webs and their influences on food chain model demand further investigations. In this paper, assuming the existence of allochthonous inputs for intermediate predator, a food chain model is formulated with disease in the prey. The stability and persistence conditions of the equilibrium points are determined. Extinction criterion for infected prey population is obtained. It is shown that suitable amount of allochthonous inputs to intermediate predator can control infectious disease of prey population, provided initial intermediate predator population is above a critical value. This critical intermediate population size increases monotonically with the increase of infection rate. It is also shown that control of infectious disease of prey is possible in some cases of seasonally varying contact rate. Dynamical behaviours of the model are investigated numerically through one and two parameter bifurcation analysis using MATCONT 2.5.1 package. The occurrence of Hopf and its continuation curves are noted with the variation of infection rate and allochthonous food availability. The continuation curves of limit point cycle and Neimark Sacker bifurcation are drawn by varying the rate of infection and allochthonous inputs. This study introduces a novel natural non-toxic method for controlling infectious disease of prey in a food chain model.

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  • Sahoo, Banshidhar & Poria, Swarup, 2015. "Effects of allochthonous inputs in the control of infectious disease of prey," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 1-19.
    • Handle: RePEc:eee:chsofr:v:75:y:2015:i:c:p:1-19
    DOI: 10.1016/j.chaos.2015.02.002
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    References listed on IDEAS

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    1. Mainul Haque & Joydev Chattopadhyay, 2007. "Role of transmissible disease in an infected prey-dependent predator -- prey system," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 13(2), pages 163-178, April.
    2. Hu, Guang-Ping & Li, Xiao-Ling, 2012. "Stability and Hopf bifurcation for a delayed predator–prey model with disease in the prey," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 229-237.
    3. Lewi Stone & Ronen Olinky & Amit Huppert, 2007. "Seasonal dynamics of recurrent epidemics," Nature, Nature, vol. 446(7135), pages 533-536, March.
    4. Sahoo, Banshidhar & Poria, Swarup, 2014. "The chaos and control of a food chain model supplying additional food to top-predator," Chaos, Solitons & Fractals, Elsevier, vol. 58(C), pages 52-64.
    5. Jana, Soovoojeet & Kar, T.K., 2013. "Modeling and analysis of a prey–predator system with disease in the prey," Chaos, Solitons & Fractals, Elsevier, vol. 47(C), pages 42-53.
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    1. Ghorai, Santu & Poria, Swarup, 2016. "Pattern formation and control of spatiotemporal chaos in a reaction diffusion prey–predator system supplying additional food," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 57-67.

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