We present a mathematical model to describe the dynamics of mosquito population when sterile male
mosquitoes (produced by irradiation) are introduced as a biological control, besides the application of
insecticide. In order to analyze the minimal effort to reduce the fertile female mosquitoes, we search
for the optimal control considering the cost of insecticide application, the cost of the production of irradiated
mosquitoes and their delivery as well as the social cost (proportional to the number of fertilized
females mosquitoes). The optimal control is obtained by applying the Pontry agin’s Maximum Principle.