Nowadays, the rapid advance of technology has brought the communication between individuals more and more accessible and diverse. This also makes people have more chance to be aware of an infectious disease outbreak and hence reduce the risk of infection. In this talk, we will introduce two different approaches to describe how individual awareness can affect the spreading of infectious diseases. The first approach is to introduce three different types of individual awareness, namely contact, local and global awareness, resulted from different sources of information, into an SIS epidemic model so that the infectious rate can be accordingly reduced. The derivation of the model is based on the microscopic Markov-chain approximation. The second is to propose a multiplex network for which the spreading of the disease and information occurs, respectively, in two different layers of networks, i.e., the physical network and the virtual network. In addition, these two diffusive processes are assumed to interact and affect each other. Such concept would create a multiplex SIS-UAU epidemic model. Some recent results on these two models are to be introduced.