Modeling the role of information and optimal control on an SEIR epidemic model with infectivity in latent period

The outbreak of a disease can lead to behavioral changes in the healthy to avert infection. We first establish a nonlinear SEIR epidemic model that incorporates the impact of individuals' behavioral response owe to information of the disease prevalence. Both the existence of equilibria and sharp sufficient conditions on stable equilibria are verified. Whereafter, the local and global sensitivity analyses are carried out to assess the relative effects of parameters on the basic reproduction number. Therewith the optimal control problem is considered to provide a theoretical basis for disease prevention and control, and the existence and uniqueness consequences for optimal control paths are demonstrated. Some numerical examples and discussions are given to support and visualize our analytical results, which can be derived that the combined use of three control measures is more effective than any single adopted control strategy to curb the spread of diseases. We also find that the information plays a crucial role in controlling infection.