Summary: We present an application of optimal control theory to Dengue epidemics. This epidemiologic disease is important in tropical countries due to the growing number of infected individuals. The dynamic model is described by a set of nonlinear ordinary differential equations, that depend on the dynamics of the Dengue mosquito, the number of infected individuals, and people’s motivation to combat the mosquito. The cost functional depends not only on the costs of medical treatment of the infected people but also on the costs related to educational and sanitation campaigns. Two approaches for solving the problem are considered: one using optimal control theory, the other carried out by first discretizing the problem and then solving it with nonlinear programming. The results obtained with OC-ODE and IPOPT solvers are given and discussed. We observe that with current computational tools it is easy to obtain, in an efficient way, better solutions to Dengue problems, leading to a decrease in the number of infected mosquitoes and individuals in less time and with lower costs.