Tesis de maestría en ciencias matemáticasDengue is an infectious tropical disease caused by the dengue virus. It is also known as breakbone fever due to the sensation the disease produces. The symptoms include fever, headache, muscle and joint pains, and a skin rash that is similar to measles which last from three to seven days. In very few cases the disease leads to a lifethreatening type of dengue called dengue hemorrhagic fever, which causes internal bleeding. Also, the dengue shock syndrome is another manifestation of the dengue disease where low blood pressure occurs which places the patient in a danger which can lead to death. Dengue is transmitted by two species of mosquitoes, Aedes aegypti type or Aedes albopictus type. Mosquitoes grow in recipients which gather clean water from rain or dew. There are four diferent strains of dengue: DEN-1, DEN-2, DEN-3, and DEN-4. Once a patient has been infected with one of these strains, he or she acquires lifetime immunity to that strain but only short-term immunity to others. These subsequent infections with diferent strains increase the risk of severe complications. Dengue disease affects mainly tropical and subtropical areas like Africa, north of Australia, and America; although lately Europe and North America have reported some cases. So far there no vaccine for dengue has been applied, but several prevention measures have been taken to reduce the effective contact of infected mosquitoes with humans and the elimination of the mosquitoes habitats.Universidad de Sonora. División de Ciencias Exactas y Naturales. Programa de Posgrado en Matemáticas, 2013 .