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Delay-induced bifurcations and chaos in a two-dimensional model for the immune response

Author

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  • Mendonça, J.P.
  • Gleria, Iram
  • Lyra, M.L.

Abstract

We consider a two-dimensional dynamical system modeling the immune response to a target population. We perform a detailed linear stability analysis to investigate possible stability switches induced by the existence of characteristic delay times of the dynamical processes, mainly a delay in the replication of the target population and delays in the stimulated and cooperative immune responses. We show that stability switches of stable periodic cycle solutions can be induced by enforcing appropriated time delays in the target reproduction as well as in the cooperative immune response. The analytical results are supported by the numerical solution of the corresponding set of delayed differential equations, showing bifurcations and quasi-chaotic behavior. We discuss the possible relevance of the present results in tailoring therapeutic strategies of viral infections exhibiting periodic viral load oscillations.

Suggested Citation

  • Mendonça, J.P. & Gleria, Iram & Lyra, M.L., 2019. "Delay-induced bifurcations and chaos in a two-dimensional model for the immune response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 484-490.
    • Handle: RePEc:eee:phsmap:v:517:y:2019:i:c:p:484-490
    DOI: 10.1016/j.physa.2018.11.039
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    Cited by:

    1. Dzyubak, Larysa & Dzyubak, Oleksandr & Awrejcewicz, Jan, 2023. "Nonlinear multiscale diffusion cancer invasion model with memory of states," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Trobia, José & de Souza, Silvio L.T. & dos Santos, Margarete A. & Szezech, José D. & Batista, Antonio M. & Borges, Rafael R. & Pereira, Leandro da S. & Protachevicz, Paulo R. & Caldas, Iberê L. & Iaro, 2022. "On the dynamical behaviour of a glucose-insulin model," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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