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The Dynamics of a Delayed Ecoepidemiological Model with Nonlinear Incidence Rate

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  • Reem Mudar Hussien
  • Raid Kamel Naji

Abstract

In this paper, the general framework for calculating the stability of equilibria, Hopf bifurcation of a delayed prey‐predator system with an SI type of disease in the prey population, is investigated. The impact of the incubation period delay on disease transmission utilizing a nonlinear incidence rate was taken into account. For the purpose of explaining the predation process, a modified Holling type II functional response was used. First, the existence, uniform boundedness, and positivity of the solutions of the considered model system, along with the behavior of equilibria and the existence of Hopf bifurcation, are studied. The critical values of the delay parameter for which stability switches and the nature of the Hopf bifurcation by using normal form theory and center manifold theorem are identified. Additionally, using numerical simulations and a hypothetical dataset, various dynamic characteristics are discovered, including stability switches, chaos, and Hopf bifurcation scenarios.

Suggested Citation

  • Reem Mudar Hussien & Raid Kamel Naji, 2023. "The Dynamics of a Delayed Ecoepidemiological Model with Nonlinear Incidence Rate," Journal of Applied Mathematics, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnljam:v:2023:y:2023:i:1:n:1366763
    DOI: 10.1155/2023/1366763
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    References listed on IDEAS

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    1. Raid Kamel Naji & Arkan N. Mustafa, 2012. "The Dynamics of an Eco-Epidemiological Model with Nonlinear Incidence Rate," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-24, October.
    2. Ahmed Sami Abdulghafour & Raid Kamel Naji, 2018. "A Study of a Diseased Prey‐Predator Model with Refuge in Prey and Harvesting from Predator," Journal of Applied Mathematics, John Wiley & Sons, vol. 2018(1).
    3. Ahmed Sami Abdulghafour & Raid Kamel Naji, 2018. "A Study of a Diseased Prey-Predator Model with Refuge in Prey and Harvesting from Predator," Journal of Applied Mathematics, Hindawi, vol. 2018, pages 1-17, December.
    4. Raid Kamel Naji & Arkan N. Mustafa, 2012. "The Dynamics of an Eco‐Epidemiological Model with Nonlinear Incidence Rate," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    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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