Outbreaks are complex multi-scale processes that are impacted not only by cellular dynamics and the ability of pathogens to effectively reproduce and spread, but also by population-level dynamics and the effectiveness of mitigation measures. A timely exchange of information related to the spread of novel pathogens, stay-at-home orders, and other containment measures can be effective at containing an infectious disease, particularly during in the early stages when testing infrastructure, vaccines, and other medical interventions may not be available at scale. Using a multiplex epidemic model that consists of an information layer (modeling information exchange between individuals) and a spatially embedded epidemic layer (representing a human contact network), we study how random and targeted disruptions in the information layer (\eg, errors and intentional attacks on communication infrastructure) impact outbreak dynamics. We calibrate our model to the early outbreak stages of the SARS-CoV-2 pandemic in 2020. Mitigation campaign can still be effective under random disruptions, such as failure of information channels between a few individuals. However, targeted disruptions or sabotage of hub nodes that exchange information with a large number of individuals can abruptly change outbreak characteristics such as the time to reach the peak infection. Our results emphasize the importance of using a robust communication infrastructure that can withstand both random and targeted disruptions.