Global monitoring of novel diseases and outbreaks is crucial for pandemic prevention. To this end, movement data from cell-phones is already used to augment epidemiological models. Recent work has posed individual cell-phone metadata as a universal data source for syndromic surveillance for two key reasons: (1) these records are already collected for billing purposes in virtually every country and (2) they could allow deviations from people's routine behaviors during symptomatic illness to be detected, both in terms of mobility and social interactions. In this paper, we develop the necessary models to conduct population-level infectious disease surveillance by using cell-phone metadata individually linked with health outcomes. Specifically, we propose GraphDNA---a model that builds Graph neural networks (GNNs) into Dynamic Network Anomaly detection. Using cell-phone call records (CDR) linked with diagnostic information from Iceland during the H1N1v influenza outbreak, we show that GraphDNA outperforms state-of-the-art baselines on individual Date-of-Diagnosis (DoD) prediction, while tracking the epidemic signal in the overall population. Our results suggest that proper modeling of the universal CDR data could inform public health officials and bolster epidemic preparedness measures.