{ "background": "Community health centres are critical for primary care delivery in sub-Saharan Africa, yet systematic evaluations of their operational efficiency and yield forecasting are limited. Existing analyses often lack robust, longitudinal methodologies to inform resource allocation and service optimisation.", "purpose and objectives": "This meta-analysis aims to methodologically evaluate published and grey literature on community health centre systems and to develop a time-series forecasting model for yield optimisation, defined as service output per unit input.", "methodology": "We conducted a systematic review and meta-analysis of studies. Quantitative data were synthesised using a random-effects model. The core forecasting model is an ARIMA(1,1,1)-GARCH(1,1) specification: $yt = \\mu + \\phi1 y{t-1} + \\theta1 \\epsilon{t-1} + \\epsilont$, with $\\sigma^2t = \\omega + \\alpha1 \\epsilon^2{t-1} + \\beta1 \\sigma^2{t-1}$, where $yt$ is the yield metric. Model uncertainty was quantified using 95% prediction intervals.", "findings": "Methodological quality was highly heterogeneous, with only 32% of studies employing longitudinal designs suitable for causal inference. The forecasting model, applied to synthesised data, projected a mean yield improvement of 18.7% (95% PI: 12.4, 25.1) under optimised conditions, with volatility clustering indicating significant operational instability.", "conclusion": "Substantial methodological gaps constrain current evidence. The developed model provides a robust tool for forecasting service yield, revealing both potential gains and systemic volatility in community health operations.", "recommendations": "Implement standardised longitudinal metrics for routine health system data. Integrate the forecasting framework into district-level planning cycles to proactively manage resources and mitigate operational volatility.", "key words": "health systems research, operational yield, time-series analysis, forecasting, primary health care, resource optimisation