SEIR epidemic model with quarantine and distributed delay: revealing the occurrence of recurrent epidemic waves

Abstract

In this paper, we deal with a SEIR epidemic model incorporating both quarantine measures and distributed time delay. We define the basic reproduction number $R_0$, and demonstrate that, when $R_0\leq 1$, the disease-free equilibrium is globally asymptotically stable. Conversely, when $R_0>1$, this equilibrium is unstable, leading to the existence of a unique endemic equilibrium. Furthermore, we investigate the occurrence of nontrivial periodic solutions that represent recurrent epidemic waves by obtaining the conditions for Hopf bifurcation. Through numerical simulations, we demonstrate the significant roles played by quarantine measures and time delays in the occurrence of recurrent epidemic waves.