Dynamics and Intermittent Stochastic Stabilization of the Epidemic-Information Coupled Propagation on Multiplex Networks

With the rapid evolution of online social media, information is exerting an influence on various aspects of human life, including the propagation of epidemics. In order to thoroughly investigate the mechanisms by which online information influences offline epidemic propagation, we propose a dual-layer propagation model, consisting of an online layer for information dissemination and a physical layer for disease transmission. Individuals who receive epidemic prevention information are likely to take more effective preventive measures, thus reducing their probability of infection. Particularly, considering the psychological impact of actual disease states on the population, we set that individuals in different states of illness will take varying degrees of preventive measures upon receiving information. We employed the next-generation matrix method to derive the threshold of the dual-layer propagation model and demonstrated the stability of the equilibrium. We also analyze the effects of information dissemination intensity and the protective strength of different population groups on the epidemic threshold. Furthermore, to control the spread of the epidemic effectively at a lower cost, we designed a nonperiodic intermittent stochastic stabilization method, utilizing exponential martingale inequalities and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\rm{It\hat o}}$</tex-math></inline-formula>’s formula to calculate the formula for the minimum control intensity derive the minimum control intensity. This strategy has the advantage of allowing flexible choices of control intensity and intervals. Numerical simulations verify the correctness of our theoretical results and the effectiveness of our control strategy.