Edge computing has emerged as a pivotal solution to meet the growing demand for real-time data processing and reduced latency in modern distributed systems. However, its decentralized nature increases the attack surface, making it vulnerable to Distributed Denial of Service (DDoS) attacks. Traditional security models, which rely on perimeter-based defenses, struggle to address these threats due to their inability to effectively manage insider threats, dynamic traffic, and sophisticated attack vectors. This paper explores the integration of Zero Trust Security Models (ZTSM) with behavioral analytics to enhance DDoS detection and mitigation in edge computing environments. Zero Trust principles, such as "never trust, always verify," enforce strict access control, continuous authentication, and micro-segmentation, reducing unauthorized access to critical resources. Behavioral DDoS detection complements this by analyzing patterns in network traffic, user behavior, and resource utilization to identify anomalies indicative of potential DDoS attacks. The proposed framework leverages machine learning algorithms to create adaptive and context-aware detection mechanisms that are scalable across edge nodes. By combining ZTSM with behavioral detection, the model offers proactive mitigation strategies, ensuring minimal disruption to edge services. This integration also addresses challenges like scalability, real-time decision-making, and false positive reduction. The study demonstrates the effectiveness of this approach through simulated DDoS scenarios in edge environments. Results indicate significant improvements in detection accuracy, response time, and overall resilience of the edge infrastructure. These findings underscore the importance of adopting Zero Trust principles and advanced behavioral analytics to safeguard edge computing systems against evolving DDoS threats. Future work will focus on enhancing model interoperability, extending the solution to heterogeneous edge environments, and incorporating predictive capabilities to anticipate and mitigate threats proactively.