We propose a novel epidemic model based on two-layered multiplex networks to explore the influence of positive and negative preventive information on epidemic propagation. In the model, one layer represents a social network with positive and negative preventive information spreading competitively, while the other one denotes the physical contact network with epidemic propagation. The individuals who are aware of positive prevention will take more effective measures to avoid being infected than those who are aware of negative prevention. Taking the microscopic Markov chain (MMC) approach, we analytically derive the expression of the epidemic threshold for the proposed epidemic model, which indicates that the diffusion of positive and negative prevention information, as well as the topology of the physical contact network have a significant impact on the epidemic threshold. By comparing the results obtained with MMC and those with the Monte Carlo (MC) simulations, it is found that they are in good agreement, but MMC can well describe the dynamics of the proposed model. Meanwhile, through extensive simulations, we demonstrate the impact of positive and negative preventive information on the epidemic threshold, as well as the prevalence of infectious diseases. We also find that the epidemic prevalence and the epidemic outbreaks can be suppressed by the diffusion of positive preventive information and be promoted by the diffusion of negative preventive information.