A SDIR (Susceptible, Displayed, Infectious and Removed)-type mathematical model was simulated which included a population of human hosts, dengue vectors, and control strategies for Aedes aegypti. The simulations indicated that applications of insecticides should be combined in both the larval and adult stages of the vector in order to quickly reduce the epidemic. In order to avoid compromising control of the mosquito, it is also necessary to use highly efficient insecticides, ensure that applications have highly effective coverage, and that they are always accompanied by constant removal of breeding sites. It is concluded that densities of the vector must be kept close to zero throughout the year to avoid the coexistence of virus and vector.