Predicting fine-grained interests of users with temporal behavior is important to personalization and information filtering applications. However, existing interest prediction methods are incapable of capturing the subtle degreed user interests towards particular items, and the internal time-varying drifting attention of individuals is not studied yet. Moreover, the prediction process can also be affected by inter-personal influence, known as behavioral mutual infectivity. Inspired by point process in modeling temporal point process, in this paper we present a deep prediction method based on two recurrent neural networks (RNNs) to jointly model each user's continuous browsing history and asynchronous event sequences in the context of inter-user behavioral mutual infectivity. Our model is able to predict the fine-grained interest from a user regarding a particular item and corresponding timestamps when an occurrence of event takes place. The proposed approach is more flexible to capture the dynamic characteristic of event sequences by using the temporal point process to model event data and timely update its intensity function by RNNs. Furthermore, to improve the interpretability of the model, the attention mechanism is introduced to emphasize both intra-personal and inter-personal behavior influence over time. Experiments on real datasets demonstrate that our model outperforms the state-of-the-art methods in fine-grained user interest prediction.