Optimal control of an epidemiological model with multiple time delays

In this paper, we consider an optimal control model governed by a system of delay differential equations representing an SIR model. We extend the model of Kaddar (2010) by incorporating the suitable controls. We consider two control strategies in the optimal control model, namely: the vaccination and treatment strategies. The model has three time delays that represent the incubation period, and the times taken by the vaccine and treatment to be effective. We derive the first-order necessary conditions for the optimal control and perform numerical simulations to show the effectiveness as well as the applicability of the model for different values of the time delays. These numerical simulations show that the model is more sensitive to the delays representing the incubation period and the treatment delay, whereas the delay associated with the vaccine is not significant.