Coronavirus disease 2019 (COVID-19) is an infectious disease with first symptoms similar to the flu. COVID-19 appeared first in China and very quickly spreads to the rest of the world, causing then the 2019-20 coronavirus pandemic. In many cases, this disease causes pneumonia. Since pulmonary infections can be observed through radiography images, this paper investigates deep learning methods for automatically analyzing query chest X-ray images with the hope to bring precision tools to health professionals towards screening the COVID-19 and diagnosing confirmed patients. In this context, training datasets, deep learning architectures and analysis strategies have been experimented from publicly open sets of chest X-ray images. Tailored deep learning models are proposed to detect pneumonia infection cases, notably viral cases. It is assumed that viral pneumonia cases detected during an epidemic COVID-19 context have a high probability to presume COVID-19 infections. Moreover, easy-to-apply health indicators are proposed for estimating infection status and predicting patient status from the detected pneumonia cases. Experimental results show possibilities of training deep learning models over publicly open sets of chest X-ray images towards screening viral pneumonia. Chest X-ray test images of COVID-19 infected patients are successfully diagnosed through detection models retained for their performances. The efficiency of proposed health indicators is highlighted through simulated scenarios of patients presenting infections and health problems by combining real and synthetic health data.