Rwanda aims to improve healthcare services, including district hospitals, by adopting time-series forecasting models for system evaluation. A systematic literature review was conducted to analyse existing studies on district hospital systems, focusing on the use of time-series forecasting techniques for system evaluation and prediction of healthcare outcomes. The analysis revealed a directionality in forecast accuracy with models showing an improvement rate of up to 30% in yield predictions over baseline methods. Time-series forecasting models can be effectively utilised to evaluate district hospital systems in Rwanda, providing insights for system optimization and performance enhancement. District hospitals should integrate time-series forecasting into their evaluation frameworks to improve healthcare outcomes and resource allocation. Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.