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A Fractional-Order Model for Zika Virus Infection with Multiple Delays

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  • R. Rakkiyappan
  • V. Preethi Latha
  • Fathalla A. Rihan

Abstract

Time delays and fractional order play a vital role in biological systems with memory. In this paper, we propose an epidemic model for Zika virus infection using delay differential equations with fractional order. Multiple time delays are incorporated in the model to consider the latency of the infection in a vector and the latency of the infection in the infected host. We investigate the necessary and sufficient conditions for stability of the steady states and Hopf bifurcation with respect to three time delays , , and . The model undergoes a Hopf bifurcation at the threshold parameters , , and . Some numerical simulations are given to show the effectiveness of obtained results. The numerical simulations confirm that combination of fractional order and time delays in the epidemic model effectively enriches the dynamics and strengthens the stability condition of the model.

Suggested Citation

  • R. Rakkiyappan & V. Preethi Latha & Fathalla A. Rihan, 2019. "A Fractional-Order Model for Zika Virus Infection with Multiple Delays," Complexity, Hindawi, vol. 2019, pages 1-20, November.
    • Handle: RePEc:hin:complx:4178073
    DOI: 10.1155/2019/4178073
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    References listed on IDEAS

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    Cited by:

    1. Suh, Jiyeon & Kwon, Hee-Dae & Lee, Jeehyun, 2024. "A model of Plasmodium vivax malaria with delays: Mathematical analysis and numerical simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 169-187.
    2. Addai, Emmanuel & Zhang, Lingling & Ackora-Prah, Joseph & Gordon, Joseph Frank & Asamoah, Joshua Kiddy K. & Essel, John Fiifi, 2022. "Fractal-fractional order dynamics and numerical simulations of a Zika epidemic model with insecticide-treated nets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    3. Ali, Hegagi Mohamed & Ameen, Ismail Gad, 2021. "Optimal control strategies of a fractional order model for Zika virus infection involving various transmissions," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    4. Naim, Mouhcine & Lahmidi, Fouad & Namir, Abdelwahed & Kouidere, Abdelfatah, 2021. "Dynamics of an fractional SEIR epidemic model with infectivity in latent period and general nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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