The recent Covid-19 pandemic has attracted significant attention toward understanding the innate immune response of humans. To develop new drugs and antibiotics that activate T-cells to combat malicious pathogens, it is necessary to comprehend the immune system, including T-cell response, peptides, and Human Leukocyte Antigens (HLA) interactions. Traditional machine learning models, such as Convolutional Neural Networks (CNNs) and Feed Forward Networks (FNNs) are limited to feature extraction of peptides to predict immunogenicity values. CNNs and FNNs cannot capture the underlying structure and relationships between HLA and peptides, and therefore, do not assist with the immune response predictions. To address these issues, firstly this paper models the Immune Epitope dataset as a graph to capture dependencies and interactions among HLAs and peptides. Secondly, to assess the performance of the graph model, the results of the Graph Neural Network (GNN) are validated against the results of FNN. The results show that the GNN has better performance efficiency over conventional models in terms of accuracy and other performance metrics, thereby recommending graph-based deep learning as an efficient tool for drug discovery, diagnosis, and other immunology.