Dynamical analysis of a fractional-order epidemic weighted network model and its finite-time control

Infectious diseases pose a major threat to public health worldwide, often leading to serious social and economic damage. It is necessary to propose an effective control method to help the disease die out quickly. Given that the weight between nodes represents the intimacy of people, which seriously affects the spread of diseases, a fractional-order epidemic model based on weighted networks is proposed. The stability properties of the system’s equilibrium points are rigorously analyzed through the application of fractional-order Lyapunov stability theory. Furthermore, a finite-time controller is proposed for application in infectious disease management. Finite-time control facilitates rapid reduction of infection rates over short durations, thereby offering a potent instrument for responding to abrupt outbreaks. This control strategy not only substantially mitigates the adverse socioeconomic impacts of the epidemic but also expedites the system’s response time, enabling control measures to more rapidly adapt to the dynamic changes in the epidemic. Finally, the validity of theoretical results is verified by simulation. • A novel fractional-order epidemic model based on weighted networks is introduced. This model considers the intimacy between individuals, represented by the weight between nodes, as a critical factor influencing disease spread. • The stability of equilibrium points in the proposed model is analyzed in-depth using fractional-order Lyapunov theory, providing a solid theoretical foundation for the model’s validity. • A finite-time controller is proposed as a solution for infectious disease control. This controller aims to rapidly reduce the infection rate within a short timeframe. • The control strategy is designed to effectively shorten the system’s response time, enabling control measures to adapt more quickly to epidemic changes. • The theoretical results have been validated through simulation, ensuring the practical applicability and effectiveness of the proposed control method.