Control of dengue disease: a case study in Cape Verde

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.