Mosquito-borne diseases continue to threaten public health, especially in densely populated tropical regions. Conventional mosquito control methods often rely on labour-intensive practices or the use of harmful chemicals, posing risks to both humans and the environment. In response, we present Dragonfly, a socially-aware mobile robot developed to autonomously manage mosquito populations in urban environments. Dragonfly attracts and traps mosquitoes using eco-friendly pheromones, reducing the need for human involvement and chemical exposure. As a socially interactive agent operating in shared public spaces, Dragonfly must navigate dynamically changing human environments without compromising human safety. A critical challenge arises: how can the robot perform mosquito control effectively without inadvertently drawing mosquitoes toward people? Existing navigation strategies prioritise collision avoidance but overlook the social and health implications of vector movement in human proximity. To tackle this, we introduce a modified predator-prey-inspired path-planning algorithm that accounts for both human crowd density and mosquito hotspots. Integrated into the A* algorithm, our approach enables Dragonfly to proactively minimise human exposure risk while reaching all mosquito hot spot regions within the time constraints. We evaluate this approach by comparing it with conventional planning methods. Results show superior performance in balancing computational efficiency, and path effectiveness. This work highlights the role of socially intelligent robotics in promoting public health, illustrating how autonomous systems can interact responsibly and safely in human-centred environments.