Disasters and the resulting emergencies are increasingly presenting situations where tele-communications infrastructure (e.g., functioning base stations) is often compromised, leading to diminished network capacity. In these situations, providing trapped populations in isolated areas with network access to be able to communicate with rescue and recovery personnel or volunteer teams is critical. Further, when network capacity is diminished, it is essential that mobile network users be alerted to “comply” and not overload the network with non-essential bandwidth-intensive traffic unrelated to the emergency unfolding. While the current evolution of the Integrated Public Alert and Warning System (IPAWS) is able to generate and disseminate such emergency alerts, there has been no analysis or evaluation of the effectiveness of such alerts as well as the design of mechanisms that can ensure such compliance to prevent network outage. In this work, we present a framework for Cognitive Public Alerts to Wireless Subscribers (CPAWS) that is able to predict and prevent mobile network overload/outage during emergencies using a mix of behavioral studies and machine learning tools that consider real-time monitoring information of the environmental status, network situation, and user compliance. Specifically, we study the efficacy of wireless emergency alerts (WEAs) in terms of saving network bandwidth by using surveys on Amazon MTurk to test the effectiveness of seven designed WEAs on reducing users' non-essential traffic across 12 designated cell phone applications. Additionally, we design complementary access and alert control strategies to ensure that the network load remains below the diminished available capacity during emergencies. CPAWS is also backward-compatible since it extends IPAWS by adding a feedback loop for real-time monitoring and control.