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Periodic solutions and chaos in a non-linear model for the delayed cellular immune response

Author

Listed:
  • Canabarro, A.A.
  • Gléria, I.M.
  • Lyra, M.L.

Abstract

We model the cellular immune response using a set of non-linear delayed differential equations. We observe that the stationary solution becomes unstable above a critical immune response time. The exponents characterizing the approach to this bifurcation point as well as the critical slow dynamics are obtained. In the periodic regime, the minimum virus load is substantially reduced with respect to the stationary solution. Further increasing the delay time, the dynamics display a series of bifurcations evolving to a chaotic regime characterized by a set of 2D portraits.

Suggested Citation

  • Canabarro, A.A. & Gléria, I.M. & Lyra, M.L., 2004. "Periodic solutions and chaos in a non-linear model for the delayed cellular immune response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 234-241.
    • Handle: RePEc:eee:phsmap:v:342:y:2004:i:1:p:234-241
    DOI: 10.1016/j.physa.2004.04.083
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    Cited by:

    1. Alfifi, H.Y., 2023. "Effects of diffusion and delayed immune response on dynamic behavior in a viral model," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    2. Alfifi, H.Y., 2024. "Stability analysis and Hopf bifurcation for two-species reaction-diffusion-advection competition systems with two time delays," Applied Mathematics and Computation, Elsevier, vol. 474(C).
    3. Haibin Wang & Rui Xu, 2013. "Stability and Hopf Bifurcation in an HIV-1 Infection Model with Latently Infected Cells and Delayed Immune Response," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-12, December.
    4. Bai, Zhenguo & Zhou, Yicang, 2012. "Dynamics of a viral infection model with delayed CTL response and immune circadian rhythm," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1133-1139.
    5. Zuo, X.Q. & Fan, Y.S., 2006. "A chaos search immune algorithm with its application to neuro-fuzzy controller design," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 94-109.
    6. John C. Eckalbar & Pete Tsournos & Walter L. Eckalbar, 2015. "Dynamics In An Sir Model When Vaccination Demand Follows Prior Levels Of Disease Prevalence," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 18(07n08), pages 1-27, November.

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