Leveraging Mathematical Models for Proactive Cybersecurity in Multi-Layered Networked Systems- A Study

In the era of increasingly complex and interconnected digital ecosystems, proactive cybersecurity has emerged as a critical requirement. This paper presents a comprehensive approach that employs advanced mathematical modeling techniques to detect, predict, and mitigate cyber threats in multi-layered networked systems. We explore and integrate methodologies from game theory, graph theory, Markov processes, control theory, and probabilistic learning to fortify defenses at the physical, network, application, and user levels. A proactive cybersecurity workflow is developed and simulated using synthetic attack data. Our results demonstrate that mathematically-informed models significantly improve risk mitigation, reduce response time, and lower the probability of successful attacks.