This study presents a C*-algebraic framework for optimizing intrusion mitigation in Internet of Things (IoT) networks by integrating mathematical models for cyberattack propagation with optimization-based security strategies. Theoretical results demonstrate that the spectral radius of the attack operator ρ(A) governs the recovery of IoT networks under attack, where ρ(A) < 1 ensures system recovery, and ρ(A) ≥ 1 leads to persistent or growing attack impact. The framework combines blockchain-based trust, AI-driven intrusion detection systems (IDS), and Zero-Trust Architecture (ZTA) to provide a multi-layered, adaptive defence system. Unlike probabilistic models that simplify attack dynamics, this approach rigorously models threats using bounded linear operators, thereby offering scalability and robustness. Optimization ensures computational efficiency, making the model suitable for resource-constrained IoT environments, with the operator norm and the spectral radius acting as key constraints. Validation on real-world datasets such as CIC-IoT2023, UNSW-NB15, and BoT-IoT revealed that the AI-IDS models achieved near-perfect performance, while the unified model integrating blockchain, IDS, and ZTA showed an accuracy of 51.0

Optimizing load balancing in cloud-based healthcare systems is critical for improving system performance, particularly in terms of reducing latency, increasing throughput, and enhancing task completion time. This study investigates the impact of optimization algorithms, specifically Genetic Algorithm (GA) and Simulated Annealing (SA), on the efficiency of cloud resource allocation in healthcare applications. Additionally, we incorporate queuing theory and stochastic processes to model the task arrival and server load dynamics. By applying these optimization techniques, the system performance was evaluated, showing significant improvements in the key performance metrics. The results highlighted a 50% improvement in latency, 50% increase in throughput, and 25% reduction in task completion time. The optimized system demonstrated enhanced resource utilization, ensuring more efficient real-time data processing in cloud healthcare environments. The proposed approach shows promising results for future applications in dynamic healthcare workload management.