@article{Lv2026, 
author = {Xiaotian Lv and Weimin Hu and Yongzhen Yun and Youhui Su},
title = {Dynamical analysis and Hopf bifurcation of an SEIR epidemic model with nonlinear incidence and time-delayed behavioral response},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {7},
pages = {5023-5039},
keywords = {SEIR model, delay differential equation, fear effect, behavioral response, Hopf bifurcation},
url = {https://www.sciopen.com/article/10.3934/era.2026222},
doi = {10.3934/era.2026222},
abstract = {In this paper, an SEIR epidemic dynamical model incorporating a fear effect, a nonlinear incidence rate, and a time-delayed behavioral response was established. The basic reproduction number        R    0   was derived using the next-generation matrix method. Theoretical analysis demonstrates that if        R          0        <  1, the disease-free equilibrium is globally asymptotically stable; if        R          0        >  1, there exists a unique endemic equilibrium, which is also globally asymptotically stable. By performing stability analysis, the critical time delay threshold        τ    0   for triggering a Hopf bifurcation was derived. Moreover theoretical analysis and numerical simulations consistently showed that when the time delay exceeds this threshold, the endemic equilibrium loses its stability and a stable limit cycle is generated, leading to periodic epidemic outbreaks. Furthermore, sensitivity analysis revealed an inverse relationship between fear coefficient    α and the critical time delay threshold        τ    0  .}
}