In this paper, we evaluate the performance and analyze the explainability of machine learning models boosted by feature selection in predicting COVID-19-positive cases from self-reported information. In essence, this work describes a methodology to identify COVID-19 infections that considers the large amount of information collected by the University of Maryland Global COVID-19 Trends and Impact Survey (UMD-CTIS). More precisely, this methodology performs a feature selection stage based on the recursive feature elimination (RFE) method to reduce the number of input variables without compromising detection accuracy. A tree-based supervised machine learning model is then optimized with the selected features to detect COVID-19active cases. In contrast to previous approaches that use a limited set of selected symptoms, the proposed approach builds the detection engine considering a broad range of features including self-reported symptoms, local community information, vaccination acceptance, and isolation measures, among others. To implement the methodology, three different supervised classifiers were used: random forests (RF), light gradient boosting (LGB), and extreme gradient boosting (XGB). Based on data collected from the UMD-CTIS, we evaluated the detection performance of the methodology for four countries (Brazil, Canada, Japan, and South Africa) and two periods (2020 and 2021). The proposed approach was assessed in terms of various quality metrics: F1score, sensitivity, specificity, precision, receiver operating characteristic (ROC), and area under the ROC curve (AUC). This work also shows the normalized daily incidence curves obtained by the proposed approach for the four countries. Finally, we perform an explainability analysis using Shapley values and feature importance to determine the relevance of each feature and the corresponding contribution for each country and each country/year.