Dengue disease, basic reproduction number and control

Abstract

Abstract\n Dengue is one of the major international public health concerns.
\nAlthough progress is underway, developing a vaccine against the disease
\nis challenging. Thus the main approach to fight the disease is vector control.
\nA model for the transmission of Dengue disease is presented.
\nIt consists of eight mutually-exclusive compartments representing the
\nhuman and vector dynamics. It also includes a control parameter (insecticide)
\nin order to fight the mosquito. The model presents three possible equilibria:
\ntwo disease-free equilibria (DFE) and another endemic equilibrium.
\nIt has been proved that a DFE is locally asymptotically stable,
\nwhenever a certain epidemiological threshold, known as the \\emph{basic reproduction number},
\nis less than one. We show that if we apply a minimum level of insecticide,
\nit is possible to maintain the basic reproduction number below unity.
\nA case study, using data of the outbreak that occurred in 2009 in Cape Verde, is presented.