The Time-Since-Infection (TSI) models have gained widespread popularity and acclaim for their performance during the COVID-19 pandemic, establishing them as an increasingly favored choice for modeling infectious disease transmission due to their simplicity, practicality, and ability to address complex disease control questions. However, this simplicity also presents a significant weakness. TSI models primarily rely on incidence data, which is a strength of the model in the early stages of pandemics when other data are not available. Still, it is also a weakness that renders the models vulnerable to fluctuations in the quality of reported infection data. We propose two different perspectives to address this challenge. The first approach involves incorporating a measurement error model and reducing parametric assumptions to account for potential data errors and model mis-specifications. The second approach involves incorporating more reliable data, e.g., hospitalization data. These efforts mark a significant step forward in infectious disease modeling using TSI models. Our improvements enhance the robustness of TSI models, enable hospitalization nowcasting, reduce bias in incidence data, and establish connections between TSI models and other infectious disease models. The models are evaluated using simulations and applied to COVID-19 data.