Since the rapid outbreak of Covid-19 and with no approved vaccines to date, profound research interest has emerged to understand the innate immune response to viruses. This understanding can help to inhibit virus replication, prolong adaptive immune response, accelerated virus clearance, and tissue recovery, a key milestone to propose a vaccine to combat coronaviruses (CoVs), e.g., Covid-19. Although an innate immune system triggers inflammatory responses against CoVs upon recognition of viruses, however, a vaccine is the ultimate protection against CoV spread. The development of this vaccine is time-consuming and requires a deep understanding of the innate immune response system. In this work, we propose a graph neural network-based model that exploits the interactions between pattern recognition receptors (PRRs), i.e., the human immune response system. These interactions can help to recognize pathogen-associated molecular patterns (PAMPs) to predict the activation requirements of each PRR. The immune response information of each PRR is derived from combining its historical PAMPs activation coupled with the modeled effect on the same from PRRs in its neighborhood. On one hand, this work can help to understand how long Covid-19 can confer immunity where a strong immune response means people already been infected can safely return to work. On the other hand, this GNN-based understanding can also abode well for vaccine development efforts. Our proposal has been evaluated using CoVs immune response dataset, with results showing an average IFNs activation prediction accuracy of 90%, compared to 85% using feed-forward neural networks.