Social networks can have asymmetric relationships. In the online social network Twitter, a follower receives tweets from a followed person but the followed person is not obliged to subscribe to the channel of the follower. Thus, it is natural to consider the dissemination of information in directed networks. In this work we use the mean-field approach to derive differential equations that describe the dissemination of information in a social network with asymmetric relationships. In particular, our model reflects the impact of the degree distribution on the information propagation process. We further show that for an important subclass of our model, the differential equations can be solved analytically.