Managing trust efficiently and effectively is critical to facilitating cooperation or collaboration and decision making tasks in tactical networks while meeting system goals such as reliability, availability, or scalability. Delay tolerant networks are often encountered in military network environments where end-to-end connectivity is not guaranteed due to frequent disconnection or delay. This work proposes a provenance-based trust framework for efficiency in resource consumption as well as effectiveness in trust evaluation. Provenance refers to the history of ownership of a valued object or information. We adopt the concept of provenance in that trustworthiness of an information provider affects that of information, and vice-versa. The proposed trust framework takes a data-driven approach to reduce resource consumption in the presence of selfish or malicious nodes. This work adopts a model-based method to evaluate the proposed trust framework using Stochastic Petri Nets. The results show that the proposed trust framework achieves desirable accuracy of trust evaluation of nodes compared with an existing scheme while consuming significantly less communication overhead.