Respiratory illnesses, such as COVID-19, pose a significant health challenge. The prompt and precise identification of pulmonary infections is essential for recognizing patients and deciding on suitable life-saving interventions. In our research, we introduce a multi-task deep learning algorithm crafted to swiftly and effectively evaluate the severity of pulmonary infections in individuals afflicted with COVID-19 or analogous respiratory ailments. Our key contributions entail suggesting a multi-task network utilizing a dual transformer encoder, accompanied by a feature fusion module that feeds two MLP regression heads. Additionally, an online amalgamation of region and score for image augmentation is employed. The consequent model quantifies chest radiographs (CXR) with two scores, characterizing the extent and opacity of infection in the lungs. Evaluation on the RALO dataset demonstrates that our multi-task approach outperforms existing prediction models, exhibiting the minimum mean absolute error and the maximum Pearson correlation coefficient during inference. These results emphasize the effectiveness of inducing two estimation scores in a multi-tasking approach for accurate lung severity diagnosis. The source code is publicly accessible at https://github.com/bouthainas/MViTReg-IP.