The field of explainable artificial intelligence (XAI) aims to build explainable and interpretable machine learning (or deep learning) methods without sacrificing prediction performance. Convolutional neural networks (CNNs) have been successful in making predictions, especially in image classification. These popular and well-documented successes use extremely deep CNNs such as VGG16, DenseNet121, and Xception. However, these well-known deep learning models use tens of millions of parameters based on a large number of pretrained filters that have been repurposed from previous data sets. Among these identified filters, a large portion contain no information yet remain as input features. Thus far, there is no effective method to omit these noisy features from a data set, and their existence negatively impacts prediction performance. In this paper, a novel interaction-based convolutional neural network (ICNN) is introduced that does not make assumptions about the relevance of local information. Instead, a model-free influence score (I-score) is proposed to directly extract the influential information from images to form important variable modules. This innovative technique replaces all pretrained filters found by trial-and-error with explainable, influential, and predictive variable sets (modules) determined by the I-score. In other words, future researchers need not rely on pretrained filters; the suggested algorithm identifies only the variables or pixels with high I-score values that are extremely predictive and important. The proposed method and algorithm were tested on real-world data set and a state-of-the-art prediction performance of 99.8% was achieved without sacrificing the explanatory power of the model. This proposed design can efficiently screen patients infected by COVID-19 before human diagnosis and can be a benchmark for addressing future XAI problems in large-scale data sets.