The effects of the local-information-driven awareness on the resource-epidemic coupled dynamics is studied in this paper. The double-layer multiplex networks are adopted to depict the coupled dynamics of the resource allocation and epidemic spreading, and a coupled model based on the modified SIS model is proposed. Through extensive Monte Carlo simulations, we find that on a network without inter-layer degree correlation, there is a cross point of the basic infection rate, when the value of the basic infection rate is lower than the cross point, the breakout of the epidemic can be postponed with the decrease of the level of awareness, while when it is larger than the point, the spread size of the epidemic can be reduced with the increase of the level of awareness. In addition, we also find that the inter-layer degree correlation can reduce the final spread size of the epidemic.