Navigating epidemic spread through multiplex networks: Unveiling turing instability and cross-diffusion dynamics

The uneven spatial distribution of populations during epidemics, particularly in light of varying infection statuses, poses significant challenges for disease management. Traditional single-layer network models have shown limitations in capturing these complexities. This study introduces a multiplex network-based epidemic model, incorporating cross-diffusion to simulate the distinct movement patterns of susceptible and infected populations. Through linear stability analysis, we identify the critical conditions precipitating Turing instability, highlighting the dual influence of network topology and cross-diffusion dynamics. Our findings underscore the role of network synchronization and structural entropy in disease transmission and spatial distribution. Utilizing mean-field theory, we elucidate the mechanisms inducing Turing instability within multiplex networks. Empirical validation using 2020’s monthly passenger traffic data and the spatial distribution of COVID-19 cases in China substantiates our theoretical insights. This research presents a robust framework for epidemic control, offering critical guidance for public health interventions, medical resource allocation, and the development of epidemic early warning systems.