Optimal control of a delayed smoking model with immigration

In this paper, we formulate a smoking model with delay and immigration, and the possibility of optimal controls both over the susceptible and heavy problem smoker subjects is assumed. The existence of the optimal control pair is also proved. We derive the optimality condition via the Pontryagin's maximum principle with delay and obtain the existence of the optimal solution. Numerical simulation is given. Numerical simulations are made to support the main results