Cough is a common symptom presenting in asthmatic children. In this investigation, an audio-based classification model is presented that can differentiate between healthy and asthmatic children, based on the combination of cough and vocalised /ɑ:/ sounds. A Gaussian mixture model using mel-frequency cepstral coefficients and constant-Q cepstral coefficients was trained. When comparing the predicted labels with the clinician's diagnosis, this cough sound model reaches an overall accuracy of 95.3%. The vocalised /ɑ:/ model reaches an accuracy of 72.2%, which is still significant because the dataset contains only 333 /ɑ:/ sounds versus 2029 cough sounds.