Optimal control analysis of a mathematical model on smoking

In this paper,the dynamics of smoking behavior under the influence of educational and media programs is modeled in the presence of two control strategies. Optimal control theory is applied to a non-linear mathematical model on smoking: impact of anti-smoking campaign which helps in obtaining time dependent case detection strategy while minimizing the cost of implementation of such strategy. We prove the existence of an optimal control set and analyze the necessary and sufficient conditions, optimality and transversality conditions. The optimality of the system is deduced analytically and solved numerically.