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Dynamic network-level models directly addressing ride-sourcing services can support the development of efficient strategies for both congestion alleviation and promotion of more sustainable mobility. Recent developments presented models focusing on ride-hailing (solo rides), but no work addressed ridesplitting (shared rides) in dynamic contexts. Here, we sought to develop a dynamic aggregated traffic network model capable of representing ride-sourcing services and background traffic in a macroscopic multi-region urban network. We combined the Macroscopic Fundamental Diagram (MFD) with detailed state-space and transition descriptions of background traffic and ride-sourcing vehicles in their activities to formulate mass conservation equations. Accumulation-based MFD models might experience additional errors due to the variation profile of trip lengths, e.g., when vehicles cruise for passengers. We integrate the so-called M-model that utilizes the total remaining distance to capture dynamics of regional and inter-regional flows and accumulations for different vehicle (private or ride-sourcing) states. This aggregated model is capable to reproduce the dynamics of complex systems without using resource-expensive simulations. We also show that the model can accurately forecast the vehicles' conditions in near-future predictions. Later, a comparison with benchmark models showed lower errors in the proposed model in all states. Finally, we evaluated the model's robustness to noises in its inputs, and forecast errors remained below 15% even where inputs were 20% off the actual values for ride-sourcing vehicles. The development of such a model prepares the path for developing real-time feedback-based management policies such as priority-based perimeter control or repositioning strategies for idle ride-sourcing vehicles and developing regulations over ride-sourcing in congested areas.