Edge/fog computing works at the local area network level or devices connected to the sensor or the gateway close to the sensor. These nodes are located in different degrees of proximity to the user, while the data processing and storage are distributed among multiple nodes. In healthcare applications in the Internet of things, when data is transmitted through insecure channels, its privacy and security are the main issues. In recent years, learning from label proportion methods, represented by inverse calibration (InvCal) method, have tried to predict the class label based on class label proportions in certain groups. For privacy protection, the class label of the sample is often sensitive and invisible. As a compromise, only the proportion of class labels in certain groups can be used in these methods. However, due to their weak labeling scheme, their classification performance is often unsatisfactory. In this article, a labeling privacy protection support vector machine using privileged information, called LPP-SVM-PI, is proposed to promote the accuracy of the classifier in infectious disease diagnosis. Based on the framework of the InvCal method, besides using the proportion information of the class label, the idea of learning using privileged information is also introduced to capture the additional information of groups. The slack variables in LPP-SVM-PI are represented as correcting function and projected into the correcting space so that the hidden information of training samples in groups is captured by relaxing the constraints of the classification model. The solution of LPP-SVM-PI can be transformed into a classic quadratic programming problem. The experimental dataset is collected from the Coronavirus disease 2019 (COVID-19) transcription polymerase chain reaction at Hospital Israelita Albert Einstein in Brazil. In the experiment, LPP-SVM-PI is efficiently applied for COVID-19 diagnosis.