The continuous data-flow application in the IoT integrates the functions of fog, edge, and cloud computing. Its typical paradigm is the E-Health system. Like other IoT applications, the energy consumption optimization of IoT devices in continuous data-flow applications is a challenging problem. Since the anomalous nodes in the network will cause the increase of energy consumption, it is necessary to make continuous data flows bypass these nodes as much as possible. At present, the existing research work related to the performance of continuous data-flow is often optimized from system architecture design and deployment. In this paper, a mathematical programming method is proposed for the first time to optimize the runtime performance of continuous data flow applications. A lightweight anomaly detection method is proposed to evaluate the reliability of nodes. Then the node reliability is input into the optimization algorithm to estimate the task latency. The latency-aware energy consumption optimization for continuous data-flow is modeled as a mixed integer nonlinear programming problem. A block coordinate descend-based max-flow algorithm is proposed to solve this problem. Based on the real-life datasets, the numerical simulation is carried out. The simulation results show that the proposed strategy has better performance than the benchmark strategy.