Complex dynamics of an SEIR epidemic model with saturated incidence rate and treatment

In this paper, we describe the dynamics of an SEIR epidemic model with saturated incidence, treatment function, and optimal control. Rigorous mathematical results have been established for the model. The stability analysis of the model is investigated and found that the model is locally asymptotically stable when R-0 < 1. The model is locally as well as globally asymptotically stable at endemic equilibrium when R-0 > 1. The proposed model may possess a backward bifurcation. The optimal control problem is designed and obtained their necessary results. Numerical results have been presented for justification of theoretical results. (C) 2017 Elsevier B.V. All rights reserved.