A novel avenue of attack against these infections involves the production and release of mosquitoes that have been genetically engineered to block the transmission of infection. Genetic modification, however, would probably result in the transgenic mosquitoes being less fit than wild-type mosquitoes: these individuals would be outcompeted and so would not spread in the wild. Genetic drive mechanisms, such as MEDEA, Wolbachia or Engineered Underdominance, have been proposed as means to overcome this fitness cost. Using population genetic models, we assess whether the use of one or more of these genetic drive mechanisms could enable a desirable transgene to become established and lead to the transgenic mosquitoes replacing the pre-existing mosquito population.