## 1 Introduction  
Flight delays pose a significant and intricate challenge to the aviation industry [1], influenced by an array of factors that are challenging to eradicate entirely. These delays have a profound impact not only on the economic well-being of passengers and airlines but also on the broader aviation ecosystem and associated industries. A single airport's operational efficiency can be compromised by delays, leading to a cascade of negative consequences such as flight postponements and cancellations. The financial toll of flight delays on the air transportation sector is staggering, with billions of dollars lost annually due to a confluence of factors, including weather conditions. The inevitability of delays is further compounded by the expanding route networks, the tension between limited airspace resources, and the increasing demands of flight scheduling, military aviation activities, and other contributing factors [2]. When a flight is delayed, it sets off a chain reaction that affects subsequent flights, creating a ripple effect that can overwhelm large airports and lead to further delays [3]. This oversaturation of airport resources can exacerbate the situation, causing delays to spread throughout the entire route network. The interconnectedness of airports and navigation points within the network means that a disruption in one link can have far-reaching effects, propagating delays throughout the system [4]. Understanding the underlying mechanisms of delay propagation is crucial for grasping the essence of flight delays. By delving into the core attributes that contribute to these delays, we can develop more effective strategies to mitigate their impact. Consequently, the analysis of flight delays has become a focal point of current research, with the potential to significantly enhance the resilience and efficiency of the aviation industry. To address the adverse effects of cascading flight delays, a multidisciplinary approach has been adopted by professionals and academics. They have delved into the realms of flight scheduling optimization [5], weather forecasting and response [6] mechanisms, air traffic management [7], and collaborative decision-making [8] within airports. While these efforts have yielded some success, they often face challenges such as lengthy development cycles and narrow applicability of findings. In this paper, we propose a novel methodology that leverages the intricacies of the actual flight route network. By simulating the spread of infectious diseases as a metaphor for flight delays, we are able to model and predict the propagation of delays throughout the network. Our approach involves identifying key nodes within the network that, when prioritized and protected, can significantly reduce the impact of flight delays. To enhance our understanding of flight delays, we utilize route network models as a tool for conducting detailed studies. This allows us to analyze the complex interdependencies within the aviation system and develop strategies that are both effective and scalable. By focusing on the protection of critical nodes, we aim to create a more resilient flight network that can better withstand and recover from operational disruptions. In the realm of route network model selection, various scholars have contributed distinct perspectives. [PERSON] and colleagues [9] introduced the dual-hub route network model, which aims to enhance route overlap optimization. However, the applicability of this model is somewhat limited, as it is primarily designed for route optimization between two specific airports. [PERSON] and his team [10] have ventured into the realm of complex network theory to develop an airline-level route network model. They have focused on data from the period of 2010 to 2019 for their model's construction. While this approach offers valuable insights, it may not be the most effective solution for addressing the delay propagation issues that are central to the focus of this paper.