  Dengue is one of the most important infectious diseases in the world, in
terms of death and economic cost. Hence, the modeling of dengue is of great
importance to help us understand the dynamics disease, and interfering with its
spreading mathematical by the proposition of control methods. In this work,
control strategies in an attempt to eliminate the Aedes aegypti mosquito, as
well as proposals for the vaccination campaign are evaluated. In our
mathematical model, the mechanical control is accomplished through the
environmental support capacity affected by a discrete function that represents
removal of breeding. Chemical control is carried out from the use of
insecticide and larvicidal. The efficacious of vaccination is studied through
the removal of a fraction of individuals, proportional to the rate of
vaccination, from the susceptible compartment and its transfer to the recovered
compartment. Our major find is that the dengue fever epidemic is only
eradicated with the use of an immunizing vaccine because control measures
directed against the vector are not enough to halt disease spreading. Even
where the infected mosquitoes are eliminated from the system, susceptible
mosquitoes are still present, and infected humans cause dengue fever to
reappear in the human population.
