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Bidirectional fractional-order dynamics of the microbiota-gut-brain axis in autism spectrum disorder featuring memory

Raed Qahiti1, Ali H Hakami1, Ahmad Albaity1

  • 1Department of Mathematics, Faculty of Science, Jazan University, 2097, Jazan, 45142, Jazan, Kingdom of Saudi Arabia.

Scientific Reports
|June 8, 2026
PubMed

Insights

New models incorporating memory effects show that Autism Spectrum Disorder (ASD) symptom persistence is underestimated. Targeting microbiota recovery and behavioral symptoms is key for effective treatment and preventing chronic pathology.

Area of Science:

  • Neuroscience
  • Systems Biology
  • Mathematical Biology

Background:

  • Conventional models of the microbiota-gut-brain axis (MGBA) in Autism Spectrum Disorder (ASD) fail to account for long-range memory effects in neuroinflammation and gut dysbiosis.
  • This oversight leads to an underestimation of symptom persistence in ASD.

Purpose of the Study:

  • To introduce a novel bidirectional fractional-order dynamical system to model memory-dependent dynamics in the MGBA of ASD.
  • To capture interactions across five key compartments: dietary antigens, gut dysbiosis, gut inflammation, neuroinflammation, and behavioral symptoms.

Main Methods:

  • Developed a fractional-order dynamical system with compartment-specific fractional orders.
  • Established system properties including existence, uniqueness, boundedness, and stability using Matignon's criterion.
  • Derived an inflammation threshold parameter and analyzed a transcritical bifurcation.
  • Performed global Sobol sensitivity analysis and formulated a fractional optimal control problem.

Main Results:

  • Identified a transcritical bifurcation at a critical inflammation threshold, distinguishing healthy recovery from chronic pathology.
  • Sensitivity analysis revealed microbiota recovery rate as crucial for preventing chronicity and behavioral recovery rate as dominant in determining symptom severity.
  • Optimal control simulations indicated triple combination therapy is superior, with direct behavioral intervention vital for symptom minimization.
  • Stronger memory effects (lower fractional order α) significantly impede therapeutic recovery.

Conclusions:

  • Ignoring memory effects in MGBA models fundamentally underestimates ASD symptom persistence.
  • The developed fractional-order model provides a more comprehensive understanding of ASD dynamics.
  • Interventions targeting microbiota and behavioral recovery, especially in combination, are essential for managing ASD symptoms effectively.
Keywords:
Autism spectrum disorderBidirectional feedbackCaputo fractional derivativeGut-brain axisInflammation dynamicsReproduction number

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