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Abstract
Dengue is one of the major international public health concerns. Although progress is underway, developing a vaccine against the disease is challenging. Thus, the main approach to fight the disease is vector control. 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 (insecticide) in order to fight the mosquito. The model presents three possible equilibria: two disease-free equilibria (DFE) and another endemic equilibrium. 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 we apply a minimum level of insecticide, it is possible to maintain the basic reproduction number below unity. A case study, using data of the outbreak that occurred in 2009 in Cape Verde, is presented.
Acknowledgements
Work partially supported by Portuguese Foundation for Science and Technology (FCT) through the PhD Grant SFRH/BD/33384/2008 (Rodrigues) and the R&D units Algoritmi (Monteiro) and CIDMA (Torres). The authors are very grateful to three referees, for valuable remarks and comments, which have contributed significantly to the quality of the paper.
