MATHEMATICAL MODELLING AND AI-DRIVEN DEFENSE MECHANISMS FOR CYBER ATTACK DYNAMICS IN SMART CITIES

The increasing deployment of smart city infrastructures, driven by the integration of Internet of Things (IoT), cyber-physical systems, and cloud-based platforms, has significantly expanded the vulnerability of urban environments to large-scale cyber attacks. In such interconnected systems, cyber threats propagate through networks in a manner analogous to epidemic processes, necessitating the development of rigorous mathematical frameworks for their analysis and control. In this study, an integer-order SEIRS (Susceptible–Exposed–Infected–Recovered–Susceptible) compartmental model is proposed to capture the transmission dynamics of cyber attacks in smart city ecosystems. The model incorporates key features such as latent infection stages, recovery, reinfection, and device turnover, thereby reflecting realistic cyber-physical interactions. A novel aspect of the proposed framework is the integration of artificial intelligence and machine learning-based adaptive defense mechanisms, which dynamically regulate critical system parameters such as infection and isolation rates. Analytical investigations include the derivation of the basic reproduction number and the establishment of both local and global stability conditions of the disease-free equilibrium through rigorous mathematical proofs. The results provide clear threshold criteria for the containment and eradication of cyber threats. Numerical simulations, calibrated to reflect emerging smart infrastructure scenarios in developing regions, demonstrate that AI-driven adaptive strategies significantly reduce infection prevalence, delay and lower peak attack intensity, and enhance overall system resilience. Sensitivity analysis further reveals that the transmission rate is the most influential parameter governing system behavior, while adaptive isolation mechanisms play a crucial role in mitigating large-scale cyber disruptions. The proposed hybrid framework, combining nonlinear dynamical systems with intelligent control, offers a robust and scalable approach for designing resilient cybersecurity architectures in smart cities. The findings contribute to bridging the gap between theoretical modeling and practical cyber defense, providing insights for the development of next-generation intelligent security systems capable of addressing the complexities of modern urban environments.