Optimal control strategy of SEIR endemic model with continuous age-structure in the exposed and infectious classes

In this paper, we consider an endemic Susceptible-Exposed-Infectious-Recovered model with continuous age-structure for exposed and infectious classes. This work is appropriate for those infectious diseases that have exposed period such as tuberculosis and herpes virus infection. Key result is the existence of an optimal control problem. To control the spread of the disease, we use an objective functional with a suitable control and present an optimal control problem. Finally, we present some simulations that support our theoretical findings and show the effectiveness of the model.