Global dynamics of a discrete SEIR epidemic model with treatment

The global dynamics of a discrete SEIR epidemic model with treatment has been considered. A unique positive solution for the proposed model with the positive initial conditions is obtained. The stability analysis of the disease-free equilibrium and endemic equilibrium have been investigated. It has been proved that the DFE is globally asymptotically stable when the basic reproduction number $\mathcal{R}_0\leq1$. The proposed model has a unique endemic equilibrium that is globally asymptotically stable whenever $\tilde{\mathcal{R}}_0>1$. The theoretical results are illustrated by a numerical simulation.