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To develop generic and reliable approaches for diagnosing and assessing the severity of COVID-19 from chest X-rays (CXR), a large number of well-maintained COVID-19 datasets are needed. Existing severity quantification architectures require expensive training calculations to achieve the best results. For healthcare professionals to quickly and automatically identify COVID-19 patients and predict associated severity indicators, computer utilities are needed. In this work, we propose a Vision Transformer (ViT)-based neural network model that relies on a small number of trainable parameters to quantify the severity of COVID-19 and other lung diseases. We present a feasible approach to quantify the severity of CXR, called Vision Transformer Regressor Infection Prediction (ViTReg-IP), derived from a ViT and a regression head. We investigate the generalization potential of our model using a variety of additional test chest radiograph datasets from different open sources. In this context, we performed a comparative study with several competing deep learning analysis methods. The experimental results show that our model can provide peak performance in quantifying severity with high generalizability at a relatively low computational cost. The source codes used in our work are publicly available at https://github.com/bouthainas/ViTReg-IP., Comment: This work has been submitted to the IEEE for possible publication