## 1 Introduction
This theoretical model is employed to analyze the development and changes in various subjects engaged in interdependent interactions. By enhancing the SIR model, they aim to improve our understanding of how different factors can influence the spread and control of infections within a network, thereby contributing to a more nuanced approach to managing network health and resilience. Traditional models of infectious disease transmission dynamics, such as the SIR, SIS (Susceptible-Infected-Susceptible), and SEIR models, provide a foundational framework for understanding the spread of diseases. However, when applying these models to the context of delay propagation within airline networks, certain limitations become apparent. The SIR [16] model, which tracks the transition of individuals from being susceptible to being infected and then recovering, does not account for a latency period. This makes it less suitable for modeling the delay propagation process in airline networks, where delays often accumulate over time. The SIS [17] model, on the other hand, assumes that flights immediately return to a susceptible state after recovery from a delay. This oversimplification neglects the impact of the accumulated delay, which can have significant repercussions on the network's performance. The SEIR [18] model, which introduces an additional latency phase (the E phase), offers a more nuanced and accurate depiction of the delay propagation process. By incorporating the E phase, the SEIR model can meticulously simulate the complexities of flight delay propagation, taking into account the latency period and the accumulation of delays. Given these considerations, this paper adopts the SEIR infectious disease model as the kinetic model for analyzing delay propagation in the airline route network. The SEIR model's ability to capture the nuances of the delay accumulation and propagation process makes it a valuable tool for understanding and potentially mitigating the spread of flight delays within the network. Once the propagation dynamics model for the route network has been established, the next critical step is to pinpoint the key nodes within the network that play a pivotal role in delay propagation. Identifying these nodes is of paramount importance, as they are typically highly connected and influential airports that can dramatically influence the velocity and extent of delay propagation throughout the network. These key nodes, often functioning as hub airports, handle a substantial volume of flight arrivals, departures, and transfers. A delay at any of these nodes can rapidly spread to other parts of the network, triggering a domino effect that escalates the risk of widespread delays across the entire route network. [PERSON] and colleagues [PERSON] and colleagues [PERSON] (2019) have employed hyper-degree to quantify the local significance of nodes, providing a method to accurately and efficiently identify nodes of importance. [PERSON] and team [PERSON] and [PERSON] (2018) have utilized the Social Network Analysis (SNA) model, an interdisciplinary approach that leverages graph theory and mathematical models to examine the relationships between social entities and to analyze the centrality and accessibility of network factors within the wind network domain. [PERSON] and co-researchers [PERSON] and others (2018) have integrated structural equilibrium theory to enhance the accuracy of network link predictions. However, these identification methods, while valuable, may not offer a comprehensive enough view to encompass the entire route network, relying primarily on topological indicators. In this paper, we propose a novel approach to key node identification by employing a GA following the simulation of delay propagation within the route network. This method allows for the optimization of key nodes, thereby enhancing the operational efficiency, route utilization, and on-time flight performance of the entire network.