High-profile, large-scale public events may be attractive targets for terrorist attacks. The security challenge for such events is exacerbated by their dynamic nature: the impact of an attack on different `targets, such as studio entrances, changes over time. In addition, the defender can relocate security resources among potential attack targets at any time, while the attacker may act at any time during the event. This study focuses on developing efficient patrolling algorithms for such dynamic domains, with continuous strategy spaces for both the defender and attacker. We propose SCOUT-A, which makes assumptions regarding relocation costs, exploits payoff representation, and computes optimal solutions efficiently. We furthermore propose SCOUT-C, to compute the exact optimal defender strategy for general cases despite the continuous strategy spaces. The experimental results demonstrate that our algorithms significantly outperform existing strategies.