Controlling Epidemics With Information Dynamics: A Neural ODE Approach

In the contemporary landscape of information dissemination, it is imperative to not only promote positive information but also to effectively manage the spread of negative content to enhance public comprehension of diseases. This study introduces an epidemiological model that integrates both positive and negative information dynamics within heterogeneous networks. Initially, we employ an activity-driven network to simulate a realistic information network, complemented by a two-layer spreading model. This model utilizes a node-central unaware-aware-unaware-susceptible-infected-susceptible (UAU-SIS) framework to delineate the microscopic diffusion dynamics. Subsequently, we propose a combined strategy that aims to inhibit the dissemination of negative information while simultaneously promoting positive messages. This approach is designed to elevate public awareness and self-protection against diseases, thereby reducing the number of infected individuals and controlling associated costs. Moreover, we employ a neural ordinary differential equation control (NODEC) mechanism to determine the optimal control signal. This method enables the learning of optimal control performance and enhances the efficiency of the solution process. The efficacy of the proposed optimal control strategy is validated through numerical simulations. The results indicate that the neural ordinary differential equation (ODE) control can effectively approximate the optimal control signals, and the strategy can significantly mitigate the final scale of infection and reduce control costs.