This work focuses on the use of a swarm of unmanned aerial vehicles (UAVs) for fire front monitoring applications. Typically, fire monitoring relies on satellite imagery or manned aircraft missions for tracking fire spread. However, both methods have limitations in terms of accuracy and safety. In this paper the authors establish a framework for cooperative, persistent tracking of a dynamic perimeter using a swarm of UAVs with an emphasis on improved accuracy and reduced delays in the tracking process. The objective is to implement a coordinated, cyclic movement of the UAVs around the evolving fire perimeter thereby facilitating efficient tracking even with a limited number of agents. An expanding closed-curve model is introduced in order to represent a growing fire and the perimeter tracking process is demonstrated using numerical simulations. The control framework comprises of two aspects: (1) radial tracking of the perimeter by each UAV based on the fire boundary it perceives within its field of view, and (2) coordinated cyclic movement of the UAVs around the growing perimeter based on artificial potential functions that govern inter-UAV dynamics. Control vectors incorporating both the aspects are implemented in this study. It is demonstrated by means of simulation results that, interestingly, the multi-agent system of UAVs converges to stable configurations under both static and dynamic perimeter tracking scenarios. Additionally, the accuracy of perimeter tracking and spatial distribution while in cyclic pursuit is investigated. The article concludes with a discussion of directions of further research.