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Message transmission in a delay-tolerant network (DTN) closely depends on the cooperation between nodes. However, nodes in real-world may be selfish so they may not be fully cooperative, and the behavior may have a certain impact on the message transmission process. Based on the famous ordinary differential equation (ODE), this paper presents the corresponding mathematical model to analyze the influence of selfish behaviors on two famous hop-limited flooding policies (lazy L-hop limited flooding and L-hop limited flooding). Then, it runs some simulations based on both synthetic and real trace and proves the exactitude of the model. The theoretical results demonstrate that the selfish behaviors significantly decrease the performance. However, if the message has a bigger lifetime, these algorithms are more robust to the selfish behaviors. In addition, the theoretical results also show that the influence depends on the network structure (the communities' number in the network). On the other hand, the location of the source also has a certain impact on the performance.