Dengue disease, basic reproduction number and control

Details Dengue disease, basic reproduction number and control Dengue disease, basic reproduction number and control

2011-03-10

arxiv.org/abs/1103.1923v1

Int. J. Comput. Math. 89 (2012), no. 3, 334--346

Mathematics

Optimization and Control

This is a preprint of a paper whose final and definitive form has appeared in International Journal of Computer Mathematics (2

Scientific paper

10.1080/00207160.2011.554540

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.

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