On application of optimal control to SEIR normalized models: Pros and cons

Abstract

In this work we normalize a SEIR model that incorporates exponential natural birth and death, as well as disease-caused death. We use optimal control to control by vaccination the spread of a generic infectious disease described by a normalized model with L-1 cost. We discuss the pros and cons of SEIR normalized models when compared with classical models when optimal control with L-1 costs are considered. Our discussion highlights the role of the cost. Additionally, we partially validate our numerical solutions for our optimal control problem with normalized models using the Maximum Principle.