SEIRS epidemic model with Caputo–Fabrizio fractional derivative and time delay: dynamical analysis and simulation

SEIRS epidemic model with Caputo–Fabrizio fractional derivative, a general incidence rate, and the time delay is considered. The main target of this work is to analyze the stability behavior and develop a numerical simulation of the fractional SEIRS model. The reproduction number $${R}_{0}$$ and the order of the fractional derivative $$\beta $$ play an important role in controlling the stability of the equilibrium points of the model, where it was shown that the disease-free equilibrium point $${P}_{0}$$ is asymptotically stable if $${R}_{0}1$$ . The proper choice of the system parameters alongside the order of differentiation guarantee that the epidemic equilibrium point $${P}_{1}$$ is asymptotically stable. The presence of a time delay in treatment and its effect on the stability behavior of the model is considered. Also, bifurcation analysis of the model depending on the time delay, $$ \beta $$ and the treatment rate is discussed. Numerical simulations based on a three-step Adams–Bashforth predictor technique for supporting and validating the theoretical results have been illustrated.