The dynamics of the SEIR epidemic model under the influence of delay

Abstract

An SEIR delayed epidemic model with nonlinear incidence and treatment rates is proposed and investigated. There is a realistic zone where the model's solutions are non-negative and bounded for all time. The stability of the two equilibrium points is explored both locally and globally. The stability and direction of Hopf-bifurcation are established using the normal form and center manifold reduction of the system. Finally, a numerical simulation to back up our analytical findings is used. The system has at most two equilibrium points, and when the delay surpasses a certain value, it exhibits a Hopf bifurcation.