The use of genetic drive mechanisms to replace native mosquito genotypes with individuals bearing antipathogen transgenes is a potential strategy for repressing insect transmission of human diseases such as malaria and dengue. Antipathogen transgenes have been developed and tested, but efficient gene drive mechanisms are lacking. Here we theoretically assess the feasibility of introducing antipathogen genes into wild Aedes aegypti populations by using a naturally occurring meiotic drive system. We consider the release of males having both a Y-linked meiotic drive gene and an X-linked drive-insensitive response allele to which an antipathogen gene is linked. We use mathematical models and computer simulations to determine how the post-introduction dynamics of the antipathogen gene are affected by specific genetic characteristics of the system. The results show that when the natural population is uniformly sensitive to the meiotic drive gene, the antipathogen gene may be driven close to fixation if the fitness costs of the drive gene, the insensitive response allele, and the antipathogen gene are low. However, when the natural population has a small proportion of an X-linked insensitive response allele or an autosomal gene that strongly reduces the effect of the drive gene, the antipathogen gene does not spread if it has an associated fitness cost. Our modeling results provide a theoretical foundation for further experimental tests.