Securing Medical IoT Devices: A Time-Delay Mathematical Approach for Cyber-Attack Detection and Mitigation

Resumo

Medical Internet of Things (MIoT) systems operate under strict latency constraints, where even brief delays in communication or cyber-incident response can significantly worsen malware spread and disrupt clinical services. This study proposes a time-delay differential equation (TDDE) model that explicitly accounts for propagation delay ( ​) and mitigation response delay ( ​) in MIoT networks, allowing delay-induced instability to be examined directly. Devices are classified into secure, compromised, and recovered states. Analytical investigation establishes the malware-free equilibrium, endemic equilibrium, and a delay-adjusted basic reproduction number ​. The analysis reveals a clear threshold structure: when , malware dies out and the system converges to a stable state, whereas  leads to sustained compromise. Numerical simulations support these findings. Minor delays result in smooth, controlled infection trajectories, while larger delays trigger oscillatory outbreaks and prolonged system degradation. Sensitivity analysis identifies infection rate, recovery effectiveness, and device turnover as key drivers of system behavior, with delays significantly amplifying their impact. These results highlight the necessity of delay-aware modeling for designing resilient MIoT cybersecurity mechanisms capable of supporting uninterrupted clinical operations. The current framework assumes homogeneous devices and fixed delays; future work should extend the model to heterogeneous network structures, time-varying delays, and hybrid TDDE–machine learning defense strategies.