title: [Mathematical model for the analysis of vaccination and vector control in malaria incidence].
abstract: OBJECTIVE
  A model describing malaria behavior through a system of ordinary differential equations.
  
  
  METHODS
  In order to construct the model, the interaction between man and the malaria vector was taken into account in different infectivity and immunity states. We also considered the vaccination effect by means of an infection blocking vaccine and parameters representing larval and adult vector control.
  
  
  RESULTS
  The model developed enables simulation of malaria disease behavior in various settings: in a natural manner without intervention, with either vector control or vaccination, and considering vector control and vaccination together.
  
  
  CONCLUSIONS
  We obtained numerical conditions for the existence of a non-trivial equilibrium state, conditioned to the existence of a single real positive root of a fourth degree polynomial. This is a problem that remains unsolved.
authors.affiliation: Programa de Matemática y Computación, Universidad del Quindío, Armenia, Colombia. juanv@uniquindio.edu.co
authors.forename: Juan U
authors.initials: JU
authors.lastname: Vásquez Pinzón
authors.forename: Stella C
authors.initials: SC
authors.lastname: Méndez-Sánchez
authors.forename: Jonny E
authors.initials: JE
authors.lastname: Duque Luna
mesh_terms: D000818:Animals; D006801:Humans; D015994:Incidence; D007303:Insect Vectors; D017780:Malaria Vaccines; D016778:Malaria, Falciparum / Q000453:epidemiology* / Q000517:prevention & control*; D008962:Models, Theoretical; D009032:Mosquito Control; D014611:Vaccination / Q000706:statistics & numerical data*
chemical_list: D017780:Malaria Vaccines