Searching for a reliable indicator of treatment response in sarcoidosis remains a challenge. The use of the soluble interleukin 2 receptor (sIL-2R) as a measure of disease activity has been proposed by researchers. A machine learning model was aimed to be developed in this study to predict sIL-2R levels based on a patient’s serum angiotensin-converting enzyme (ACE) levels, potentially aiding in lung function evaluation. A novel forecasting model (SVR-BE-CO) for sIL-2R prediction is introduced, which combines support vector regression (SVR) with a hybrid optimization model (BES-CO); The hybrid optimization model composed of Bald Eagle Optimizer (BES) and Chimp Optimizer (CO) model. In this forecasting model, the hyper-parameters of the SVR model are optimized by the BES-CO hybrid optimization model, ultimately improving the accuracy of the predicted sIL-2R values. The hybrid forecasting model SVR-BE-CO model was evaluated against various forecasting methods, including Hybrid SVR with Firefly Algorithm (SVR-FFA), decision tree (DT), SVR with Gray Wolf Optimization (SVR-GWO) and random forest (RF). It was demonstrated that the hybrid SVR-BE-CO model surpasses all other methods in terms of accuracy.