Dynamics of an fractional SEIR epidemic model with infectivity in latent period and general nonlinear incidence rate

In this paper, we consider an fractional SEIR epidemic model with infectious force in the latent period and general nonlinear incidence rate of the form f(S,I)I+g(S,E)E. The global existence, nonnegativity and boundedness of solutions in this system are proved. The basic reproduction number is obtained. We show that the model exhibits two equilibriums: the disease-free and endemic equilibrium. The local stability of each equilibrium are discussed. By means of Lyapunov functionals and LaSalle’s invariance principle, we proved the global asymptotic stability of the equilibria. An application is given and numerical simulation results have been incorporated to support the theoretical results of this work.