Genetic approaches for controlling disease vectors have aimed either to reduce wild-type populations or to replace wild-type populations with insects that cannot transmit pathogens. Here, we propose a Reduce and Replace (R&R) strategy in which released insects have both female-killing and anti-pathogen genes. We develop a mathematical model to numerically explore release strategies involving an R&R strain of the dengue vector Aedes aegypti. We show that repeated R&R releases may lead to a temporary decrease in mosquito population density and, in the absence of fitness costs associated with the anti-pathogen gene, a long-term decrease in competent vector population density. We find that R&R releases more rapidly reduce the transient and long-term competent vector densities than female-killing releases alone. We show that releases including R&R females lead to greater reduction in competent vector density than male-only releases. The magnitude of reduction in total and competent vectors depends upon the release ratio, release duration, and whether females are included in releases. Even when the anti-pathogen allele has a fitness cost, R&R releases lead to greater reduction in competent vectors than female-killing releases during the release period; however, continued releases are needed to maintain low density of competent vectors long-term. We discuss the results of the model as motivation for more detailed studies of R&R strategies.