In this paper, we investigate the qualitative behavior of a class of fractional SEIR epidemic models with a more general incidence rate function and time delay to incorporate latent infected individuals. We first prove positivity and boundedness of solutions of the system. The basic reproduction number  0 of the model is computed using the method of next generation matrix, and we prove that if  0 < 1, the healthy equilibrium is locally asymptotically stable, and when  0 > 1, the system admits a unique endemic equilibrium which is locally asymptotically stable. Moreover, using a suitable Lyapunov function and some results about the theory of stability of differential equations of delayed fractional-order type, we give a complete study of global stability for both healthy and endemic steady states. The model is used to describe the COVID-19 outbreak in Algeria at its beginning in February 2020. A numerical scheme, based on Adams-Bashforth-Moulton method, is used to run the numerical simulations and shows that the number of new infected individuals will peak around late July 2020. Further, numerical simulations show that around 90% of the population in Algeria will be infected. Compared with the WHO data, our results are much more close to real data. Our model with fractional derivative and delay can then better fit the data of Algeria at the beginning of infection and before the lock and isolation measures. The model we propose is a generalization of several SEIR other models with fractional derivative and delay in literature.

In the present paper we investigate the qualitative behaviour of a fractional SEIR model with general incidence rate function and time delay where the fractional derivative is defined in the Caputo sense. The basic reproduction number $\mathcal{R}_{0}$ is derived using the method of next generation matrix and we give a complete study of local stability of both free and endemic equilibrium. Using Liapunov method we prove the global stability of free and endemic equilibrium under some hypotheses on the parameters of the system. Finally to illustrate our results, we use the model to predict the first peak of the COVID-19 epidemic in Algeria.