With the explosive development of the Internet of Things (IoT), it is convenient and important to collect health data from medical sensors and smart devices and construct medical knowledge graph. The knowledge graph contributes to investigating the connection between patient and disease, especially for epidemic surveillance. However, it is possible to cause the leakage of sensitive health information due to the untrusted data collector or various malicious attackers. In this paper, we attempt to utilise federated learning to construct a special knowledge graph, that is, individual-symptom relationship diagram with local differential privacy (LDP-ISRD), for epidemic risk surveillance, which presents the underlying infectious relationship among individuals. At first, we propose a federated learning-based framework of LDP-ISRD by utilising individuals' smart devices in IoT. Then, we leverage locations to determine the connection among individuals in terms of physical contact. Next, we propose a randomised algorithm PrivISRD to implement federated learning-based LDP-ISRD, which consists of symptom perturbation and aggregation. Finally, extensive experiments evaluate the impact of various parameters and results demonstrate that LDP-ISRD has good performance.