This study presents a hybrid digital twin system designed for real-time indoor air quality (IAQ) monitoring and filtration optimization within a residential environment. Using a network of low-cost sensors, physics-based simulations, and machine learning models, the system dynamically replicates the indoor environment to enable continuous assessment and optimization of key pollutants, including particulate matter, volatile organic compounds, and carbon dioxide. The system architecture integrates mass balance and decay models, computational fluid dynamics simulations, regression models, and neural network algorithms, all evaluated under both filtering and non-filtering conditions. A graphical user interface allows users to interact with the system, test air purifier placements, and visualize air quality dynamics in real time. The results demonstrate that, within this system, simpler models, such as linear regression, outperform more complex architectures under data-limited conditions, achieving test-set coefficients of determination ranging from 0.97 to 0.99 across multiple IAQ parameters. At the same time, the hybrid modelling approach enhances interpretability and robustness. Overall, this digital twin system contributes to smart building management by offering a scalable, interpretable, and cost-effective solution for proactive IAQ control and personalized decision-making.