  A model for the transmission of dengue disease is presented. It consists of
eight mutually-exclusive compartments representing the human and vector
dynamics. It also includes a control parameter (adulticide spray) in order to
combat the mosquito. The model presents three possible equilibria: two
disease-free equilibria (DFE) --- where humans, with or without mosquitoes,
live without the disease --- and another endemic equilibrium (EE). In the
literature it has been proved that a DFE is locally asymptotically stable,
whenever a certain epidemiological threshold, known as the basic reproduction
number, is less than one. We show that if a minimum level of insecticide is
applied, then it is possible to maintain the basic reproduction number below
unity. A case study, using data of the outbreak that occured in 2009 in Cape
Verde, is presented.
