Fractional-order $\mathcal{SEIR}$ epidemic model with time delay and saturated incidence rate


Fatima Cherkaoui, Khalid Hilal, Abdelaziz Qaffou, Shahram Rezapour, Mohammad Esmael Samei




In this study, we examine the qualitative behavior of a fractional $\mathcal{SEIR}$ model with nonlinear incidence rate function and a time delay, where the fractional derivative is defined in the sense of Caputo. The threshold parameter, $\mathcal{R}_0$ is obtained by using the method of next generation matrix and we give a complete study of existence of steady state. To establish the global stability of both the disease-free and endemic equilibria, we primarily apply the Lyapunov functional approach throughout the work. Finally, numerical simulations that exemplify our theoretical results are given.