In this work we consider an epidemic model that contains four species susceptible, exposed, infected and quarantined. With this model, first we find a feasible region which is invariant and where the solutions of our model are positive. Then the persistence of the model and sufficient conditions associated with extinction of infection population are discussed. To show that the system is locally asymptotically stable, a Lyapunov functional is constructed. After that, taking the delay as the key parameter, the conditions for local stability and Hopf bifurcation are derived. Further, we estimate the properties for the direction of the Hopf bifurcation and stability of the periodic solutions. Finally, some numerical simulations are presented to support our analytical results.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.