Mathematics – Optimization and Control
Scientific paper
2010-06-30
Proceedings of the 10th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2
Mathematics
Optimization and Control
7 pages, 4 figures. Presented at the 10th International Conference on Computational and Mathematical Methods in Science and En
Scientific paper
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.
Monteiro Teresa M. T.
Rodrigues Helena Sofia
Torres Delfim F. M.
Zinober Alan
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