<p dir="ltr">Safety and explainability are a top priority across many real-world applications of control in safety-critical systems. Networked dynamic systems are one sub-class of models that encompass many of the safety-critical systems in need of such safety guarantees. In this dissertation, we present our work in the safety-critical control of general non-networked epidemic processes, as well as our work on the modeling and analysis of networked epidemic-spreading processes. We then present a framework for the safety-critical control of networked dynamic systems including individual node vulnerability analysis and a CBF-based collaborative-safety condition. We develop a collaborative-safety framework that leverages high-order barrier functions to encode the effect of neighbors on individual safety requirements and demonstrate how this framework can be used in both epidemic models and in formation control problems. We provide an analysis on the finite-time convergence rate of our collaborative-safety algorithm in the special case of a tree structure network for a formation control application. Finally, we provide some concluding remarks and discussion on important directions for future work in the field of collaborative control for multi-agent autonomous systems.</p>