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Exploring dynamical complexity in a time-delayed tumor-immune model.

Parthasakha Das1, Ranjit Kumar Upadhyay2, Pritha Das1

  • 1Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India.

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This study reveals that incorporating time delays in tumor-immune models enhances dynamical complexity, potentially indicating long-term cancer relapse. Analyzing complexity offers insights into cancer biology and disorder.

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Area of Science:

  • Mathematical Biology
  • Computational Biology
  • Nonlinear Dynamics

Background:

  • Dynamical complexity analysis quantifies structural disorder in nonlinear phenomena.
  • Mathematical models of tumor-immune interactions offer insights into cancer biology.

Purpose of the Study:

  • To explore dynamical complexity in a time-delayed tumor-immune model.
  • To investigate the relationship between model complexity and cancer relapse.
  • To understand the role of interleukin-2 and time delays in tumor-immune dynamics.

Main Methods:

  • Bifurcation analyses in various parametric regimes.
  • The 0-1 test for chaoticity.
  • One- and two-parameter bifurcation diagrams.
  • Weighted recurrence entropy for quantifying asymptotic behavior.

Main Results:

  • The onset of chaos was predicted and manifested by multi-periodicity.
  • Dynamical complexity was quantified and linked to the system's asymptotic behavior.
  • Incorporating time delays in interleukin's effect significantly enhanced dynamical complexity.

Conclusions:

  • Dynamical complexity in tumor-immune models can signify long-term cancer relapse.
  • Time delays in interleukin effects are crucial for enhancing tumor-immune interplay complexity.
  • This research provides a framework for understanding cancer dynamics through complexity analysis.