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Conservation of a predator species in SIS prey-predator system using optimal taxation policy

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  • Juneja, Nishant
  • Agnihotri, Kulbhushan

Abstract

In this paper, we present and analyze a prey-predator system, in which prey species can be infected with some disease. The model presented in this paper is motivated from D. Mukherjee’s model in which he has considered an SI model for the prey species. There are substantial evidences that infected individuals have the ability to recover from the disease if vaccinated/ treated properly. In this regard, Mukherjee’s model is modified by considering SIS model for prey species. Theoretical and numerical simulations show that the recovery of infected prey species plays a crucial role in eliminating the limit cycle oscillations and thus making the interior equilibrium point stable. The possibility of Hopf bifurcation around non zero equilibrium point using the recovery rate as a bifurcation parameter, is discussed. Further, the model is extended by incorporating the harvesting of predator population. A monitory agency has been introduced which monitors the exploitation of resources by implementing certain taxes for each unit biomass of the predator population. The main purpose of the present research is to explore the effect of recovery rate of prey on the dynamics of the system and to optimize the total economical net profits from harvesting of predator species, taking taxation as control parameter.

Suggested Citation

  • Juneja, Nishant & Agnihotri, Kulbhushan, 2018. "Conservation of a predator species in SIS prey-predator system using optimal taxation policy," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 86-94.
    • Handle: RePEc:eee:chsofr:v:116:y:2018:i:c:p:86-94
    DOI: 10.1016/j.chaos.2018.09.024
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    References listed on IDEAS

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    1. Juneja, Nishant & Agnihotri, Kulbhushan & Kaur, Harpreet, 2018. "Effect of delay on globally stable prey–predator system," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 146-156.
    2. Hai-Feng Huo & Hui-Min Jiang & Xin-You Meng, 2012. "A Dynamic Model for Fishery Resource with Reserve Area and Taxation," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-15, January.
    3. 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.
    4. Lajmiri, Z. & Khoshsiar Ghaziani, R. & Orak, Iman, 2018. "Bifurcation and stability analysis of a ratio-dependent predator-prey model with predator harvesting rate," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 193-200.
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    Cited by:

    1. Agnihotri, Kulbhushan & Kaur, Harpreet, 2021. "Optimal control of harvesting effort in a phytoplankton–zooplankton model with infected zooplankton under the influence of toxicity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 946-964.
    2. Mingjing Du & Junmei Li & Yulan Wang & Wei Zhang, 2019. "Numerical Simulation of a Class of Three-Dimensional Kolmogorov Model with Chaotic Dynamic Behavior by Using Barycentric Interpolation Collocation Method," Complexity, Hindawi, vol. 2019, pages 1-14, April.

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