TITLE:
Hopf Bifurcation Analysis of Fractional SEIR Model with Double Time Delays
AUTHORS:
Fuhong Zhang, Xiaolan Liu
KEYWORDS:
Hopf Bifurcation, Fractional-Order Delayed SEIR, Stability
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.9,
September
14,
2026
ABSTRACT: If a natural disaster like the epidemic breaks out again, we all know that the consequences will be unimaginable. In order to describe the transmission process of infectious diseases more vividly, this paper constructs a new fractional-order SEIR model, and introduces two time-delay parameters: incubation period and recovery period. For this system, we calculate two equilibrium points, and focus on the stability of the local equilibrium point affected by time delay and hopf bifurcation. Finally, we calculate the critical time delay through the numerical calculator maple, and verify the local asymptotic stability at the equilibrium point and the result of hopf bifurcation through numerical simulation.