Natural disasters have a significant impact on human welfare. In recent years, disasters are more violent and frequent due to climate change, so their impact may be higher if no preemptive measures are taken. In this context, real-time data processing and analysis have shown great potential to support decision-making, rescue, and recovery after a disaster. However, disaster scenarios are challenging due to their highly dynamic nature. In particular, we focus on data traffic and available processing resources. In this work, we propose SLedge—an edge-based processing model that enables mobile devices to support stream processing systems’ tasks under post-disaster scenarios. SLedge relies on a two-level control loop that automatically schedules SPS’s tasks over mobile devices to increase the system’s resilience, reduce latency, and provide accurate outputs. Our results show that SLedge can outperform a cloud-based infrastructure in terms of latency while keeping a low overhead. SLedge processes data up to five times faster than a cloud-based architecture while improving load balancing among processing resources, dealing better with traffic spikes, and reducing data loss and battery drain.