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Stability analysis and Hopf bifurcation in a time-delayed fractional epidemic model

Author

Listed:
  • Feng, Xiaozhou
  • Lei, Yang
  • Xie, Fei
  • Li, Changtong
  • Wang, Yuzhen
  • Wang, Xiaojia
  • Li, Tingting

Abstract

This paper investigates a time-delayed fractional SIR epidemic model incorporating a saturated incidence rate. First, the existence of endemic equilibria is investigated under different conditions, and the basic reproduction number is calculated utilizing the next-generation matrix method. Then, the global and local asymptotic stability of equilibrium points are analyzed. For the time delay τ=0, global asymptotic stability conditions are obtained by constructing a Lyapunov function. Finally, through Hopf bifurcation analysis, the influence of the fractional order on the system’s dynamic behavior is discussed. This study provides epidemiological insights that inform practical measures for managing infectious disease outbreaks: (i) During the initial epidemic stage, it is crucial to minimize the response delay to prevent exceeding the critical bifurcation threshold; (ii) The stability of epidemic containment systems can be significantly enhanced by adjusting the fractional order appropriately.

Suggested Citation

  • Feng, Xiaozhou & Lei, Yang & Xie, Fei & Li, Changtong & Wang, Yuzhen & Wang, Xiaojia & Li, Tingting, 2026. "Stability analysis and Hopf bifurcation in a time-delayed fractional epidemic model," Applied Mathematics and Computation, Elsevier, vol. 515(C).
    • Handle: RePEc:eee:apmaco:v:515:y:2026:i:c:s0096300325005880
    DOI: 10.1016/j.amc.2025.129863
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    References listed on IDEAS

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    4. Yakui Xue & Tiantian Li, 2013. "Stability and Hopf Bifurcation for a Delayed SIR Epidemic Model with Logistic Growth," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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