<p>Sinkhole attacks pose a serious threat to the reliability, security, and performance of IoT networks by maliciously attracting and misdirecting network traffic. While many studies focus on detecting or preventing such attacks using trust systems, anomaly detection, or machine learning, there is a clear lack of research that quantitatively models their impact on network performance. This work presents a novel mathematical modeling framework to analyze how sinkhole attacks degrade IoT networks over time. Unlike prior work that mainly targets mitigation, our model offers an analytical perspective capturing the dynamic effects and network-wide consequences of these attacks. The proposed model assesses four key metrics: Packet Delivery Ratio (PDR), End-to-End Delay, Traffic Congestion, and Throughput to quantify the impact of sinkhole attacks. Results show that PDR drops from 95% to 20% within 40, 90, and 200 seconds when a single sinkhole is positioned at levels 2, 5, and 10, respectively. With three sinkholes, the same degradation occurs faster within 12.5, 25, and 70 seconds. End-to-end delay increases from 0.3 to 1.1 seconds, while throughput sharply declines from 2.4 Mbps to 0.1 Mbps within 30 seconds. Traffic congestion near attacker nodes intensifies, with packet loads rising from 400 to over 900, revealing how attack position and density accelerate network performance collapse. By presenting the first formal mathematical model of sinkhole attack impact experimentally verified through simulation, this study helps researchers and practitioners better understand the dynamic effects of such attacks on IoT networks and lays the foundation for developing more resilient and performance aware security strategies.</p>