Optimal Control for an SEIR Epidemic Model with Nonlinear Incidence Rate

The objective of this paper is to explore possible impacts of nonlinearity of functional responses and a number of compartments of an infection disease model on principal qualitative properties of the optimal controls. To address this issue, we consider optimal controls for an Susceptible-Exposed-Infectious-Removed (SEIR) model of an endemically persisting infectious disease. We assume that the incidence rate is given by an unspecified nonlinear function constrained by a few biologically motivated conditions. For this model, we consider five controls (which comprise all controls that are possible for this model) with a possibility of acting simultaneously, and establish principal qualitative properties of the controls. A comparison with a similar SIR model is provided.