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Study of an eco-epidemiological model with Z-type control

Author

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  • Alzahrani, Abdullah K.
  • Alshomrani, Ali Saleh
  • Pal, Nikhil
  • Samanta, Sudip

Abstract

In the present paper, an eco-epidemic model with Z-type control mechanism has been proposed and analyzed. We consider a predator-prey model with Holling type-II functional response, where prey is subjected to disease infection. We observe that disease may destabilize the system by producing chaotic oscillations. To confirm the occurrence of chaos, we draw the Poincare map and also compute the Lyapunov exponents. We further observe that if the indirect Z-controller is applied in the predator population, then the chaos as well as the disease can be eliminated from the system. To explore the global dynamics of the system and the possible applications of Z-type control mechanism, we perform extensive numerical experiments.

Suggested Citation

  • Alzahrani, Abdullah K. & Alshomrani, Ali Saleh & Pal, Nikhil & Samanta, Sudip, 2018. "Study of an eco-epidemiological model with Z-type control," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 197-208.
    • Handle: RePEc:eee:chsofr:v:113:y:2018:i:c:p:197-208
    DOI: 10.1016/j.chaos.2018.06.012
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    References listed on IDEAS

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    1. Neil M. Ferguson & Christl A. Donnelly & Roy M. Anderson, 2001. "Transmission intensity and impact of control policies on the foot and mouth epidemic in Great Britain," Nature, Nature, vol. 413(6855), pages 542-548, October.
    2. Saifuddin, Md. & Biswas, Santanu & Samanta, Sudip & Sarkar, Susmita & Chattopadhyay, Joydev, 2016. "Complex dynamics of an eco-epidemiological model with different competition coefficients and weak Allee in the predator," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 270-285.
    3. David M. Morens & Gregory K. Folkers & Anthony S. Fauci, 2004. "The challenge of emerging and re-emerging infectious diseases," Nature, Nature, vol. 430(6996), pages 242-249, July.
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    Cited by:

    1. Bashkirtseva, Irina & Ryashko, Lev & Ryazanova, Tatyana, 2020. "Analysis of regular and chaotic dynamics in a stochastic eco-epidemiological model," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    2. Lacitignola, Deborah & Diele, Fasma, 2021. "Using awareness to Z-control a SEIR model with overexposure: Insights on Covid-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Gupta, Ashvini & Dubey, Balram, 2022. "Bifurcation and chaos in a delayed eco-epidemic model induced by prey configuration," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    4. Mandal, Dibyendu Sekhar & Chekroun, Abdennasser & Samanta, Sudip & Chattopadhyay, Joydev, 2021. "A mathematical study of a crop-pest–natural enemy model with Z-type control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 468-488.
    5. Senapati, Abhishek & Panday, Pijush & Samanta, Sudip & Chattopadhyay, Joydev, 2020. "Disease control through removal of population using Z-control approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).

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