Understanding and mitigating the rapid spread of infectious diseases requires innovative mathematical tools that capture the complexity of real-world human interactions. This research project develops novel stochastic mathematical models that combine queueing theory and advanced probabilistic methods to shed a new light on how diseases propagate within service systems and broader social networks. By quantifying personalized infection risk in crowded environments such as hospitals and transportation systems, these models reveal how quickly a single infected individual can trigger widespread outbreaks in service systems. Furthermore, analyzing infectious disease spread in queueing systems offers valuable insights into side-channel attacks in cybersecurity. In particular, cryptographic operations can be modeled as tasks in a queue, with processing times influenced by factors such as data or device characteristics. Attackers exploit these time variations to extract sensitive information, such as cryptographic keys. By treating security systems as queues, the mathematical models in this proposal can help reveal potential information leakage, thereby contributing to the design of more robust cybersecurity measures. The resulting insights from this work will empower public health officials to make data-driven and model-driven decisions, which will ultimately reduce spread and optimize resource allocation during subsequent health crises, and also provide a framework for understandin