Millions of people have died worldwide from COVID-19. In addition to its high death toll, COVID-19 has led to unbearable suffering for individuals and a huge global burden to the healthcare sector. Therefore, researchers have been trying to develop tools to detect symptoms of this human-transmissible disease remotely to control its rapid spread. Coughing is one of the common symptoms that researchers have been trying to detect objectively from smartphone microphone-sensing. While most of the approaches to detect and track cough symptoms rely on machine learning models developed from a large amount of patient data, this is not possible at the early stage of an outbreak. In this work, we present an incremental transfer learning approach that leverages the relationship between healthy peoples' coughs and COVID-19 patients' coughs to detect COVID-19 coughs with reasonable accuracy using a pre-trained healthy cough detection model and a relatively small set of patient coughs, reducing the need for large patient dataset to train the model. This type of model can be a game changer in detecting the onset of a novel respiratory virus.