Modeling Distributed Denial-of-Service Attacks toDevelop Defensive Strategies in the Internetof Everything

As smart devices become increasingly interconnected through the Internet, the Internet of Everything (IoE) has emerged as a foundational aspect of modern life, supporting convenience, automation, and energy management. However, many IoE devices lack sufficient security mechanisms, making them vulnerable targets for cyberattacks, particularly Distributed Denial-of-Service (DDoS) attacks. This research proposes a mathematical modeling framework to analyze and simulate the behavior of DDoS attacks in IoE environments. A modified SIR(Susceptible-Infected-Recovered) model is employed to represent device state transitions, combined with assumptions about traffic volume and device capacity, as well as theoretical theorems for developing effective defense strategies. Simulation results reveal that when the basic reproduction number 𝑅0 = 𝛽∕𝛾 exceeds 1, the system experiencesrapid propagation of the attack, with the number of compromised devices increasing significantly before recoveringthrough isolation mechanisms. Three defense strategies were compared: no defense, static defense with 𝛿 = 0.33, andadaptive defense that adjusts dynamically based on the infection level. The results show that without defense, the system is overwhelmed and fails. Static defense fully mitigates the attack but consumes a constant level of resources. Incontrast, adaptive defense effectively reduces system impact using significantly fewer resources by scaling mitigationbased on real-time threats. Visualizations such as phase diagrams, heatmaps, and cumulative cost graphs confirm thetheoretical findings and illustrate the dynamics clearly. This study concludes that mathematical modeling, combinedwith dynamic control strategies, can significantly improve the resilience of IoE systems against DDoS attacks. Thevalidated approach offers a practical foundation for designing scalable and adaptive cybersecurity solutions for futureIoT and IoE infrastructures