The rapid spread of rumors on social media has posed significant challenges to maintaining public trust and information integrity. Since an information cascade process is essentially a propagation tree, recent rumor detection models leverage graph neural networks to additionally capture information propagation patterns, thus outperforming text-only solutions. Given the variations in topics and social impact of the root node, different source information naturally has distinct outreach capabilities, resulting in different heights of propagation trees. This variation, however, impedes the data-driven design of existing graph-based rumor detectors. Given a shallow propagation tree with limited interactions, it is unlikely for graph-based approaches to capture sufficient cascading patterns, questioning their ability to handle less popular news or early detection needs. In contrast, a deep propagation tree is prone to noisy user responses, and this can in turn obfuscate the predictions. In this paper, we propose a novel Epidemiology-informed Network (EIN) that integrates epidemiological knowledge to enhance performance by overcoming data-driven methods sensitivity to data quality. Meanwhile, to adapt epidemiology theory to rumor detection, it is expected that each users stance toward the source information will be annotated. To bypass the costly and time-consuming human labeling process, we take advantage of large language models to generate stance labels, facilitating optimization objectives for learning epidemiology-informed representations. Our experimental results demonstrate that the proposed EIN not only outperforms state-of-the-art methods on real-world datasets but also exhibits enhanced robustness across varying tree depths.