The pervasiveness of the Internet and smartphones enables individuals to participate in online social networks such Twitter and Facebook, besides the classic physical contact network. Such multi-layer network allows for feedback between networks / layers. For instance, the spread of a biological disease such as Ebola in a physical contact network may trigger the spreading of the information related to this disease in online social networks. The information propagated online may increase the alertness of some individuals resulting in avoidance of the physical contact with infected members in the physical contact network, which possibly protects the population from the infection. In this thesis, we propose two models for studying not only epidemic spreading and information propagation, but also the interactions between the epidemic and information. We explore two key factors that may influence the performance of such epidemic mitigation via awareness propagation: (i) the time scale of the epidemic information propagation in online social network relative to that of the epidemic spreading in physical contact network, or equivalently, the information update frequency in the social network, and (ii) the structure of the multi-layer networks. Contrary to our intuition, we find that very frequent information updates in an online social network sometimes reduce the mitigation effect when using awareness information. Such mitigation tends to perform better when the physical contact network and the online social network overlap more. We explain these findings analytically, with the help of our original Individual-Based Mean Field Approximation IBMFA. Moreover, we derive the analytical approach Microscopic Markov Chain Approach MMCA according to our models. We show that IBMFA is a better approximation than the MMCA in some scenarios, especially around the epidemic threshold. Our results indicate that the optimum effect of epidemic mitigation does not require very frequent information updates in an online social network which dilute the alertness information and therefore reduce the effect of mitigation, whereas encouraging individuals to keep in touch with their physical contacts as well online is beneficial for the mitigation.