Motivated by the failure of current methods to control dengue fever, we formulate a mathematical model to assess the impact on the spread of a mosquito-borne viral disease of a strategy that releases adult male insects homozygous for a dominant, repressible, lethal genetic trait. A dynamic model for the female adult mosquito population, which incorporates the competition for female mating between released mosquitoes and wild mosquitoes, density-dependent competition during the larval stage, and realization of the lethal trait either before or after the larval stage, is embedded into a susceptible-exposed-infectious- susceptible human-vector epidemic model for the spread of the disease. For the special case in which the number of released mosquitoes is maintained in a fixed proportion to the number of adult female mosquitoes at each point in time, we derive mathematical formulas for the disease eradication condition and the approximate number of released mosquitoes necessary for eradication. Numerical results using data for dengue fever suggest that the proportional policy outperforms a release policy in which the released mosquito population is held constant, and that eradication in approximately 1 year is feasible for affected human populations on the order of 105 to 106, although the logistical considerations are daunting. We also construct a policy that achieves an exponential decay in the female mosquito population; this policy releases approximately the same number of mosquitoes as the proportional policy but achieves eradication nearly twice as fast.