Dengue disease, basic reproduction number and control

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.