There are so many areas where Deep Learning (DL) can be applied in the medicine field. Such as, (Identification/detection/recognizing) of a disease based on images, like brain cancer. Convolution Neural Networks (CNNs) are used to extract the features, analyze, and classify the images and determine whether the patient has cancer or not.
One more example, the chat bot which has the ability of analyzing the conversation between the patient and the device, it can determines whether he/she has a disease or not. Google Assistant is a great machine learning example and can be modified and used as a personal doctor.
For more info, you can refer to some well-known projects, such as Google's DeepMind Health
Deep learning is a special subset of machine learning, made possible with the advent of big data in medicine and healthcare. In a recent NPJ Digital Medicine article (available at https://www.nature.com/articles/s41746-018-0061-1 ), Kolachalama and Garg argue that "educating the next generation of medical professionals with the right (machine learning) techniques will enable them to become part of this emerging revolution. Yet, the medical school curriculum as well as the graduate medical education and other teaching programs within academic hospitals across the United States and around the world have not yet come to grips with educating students and trainees on this emerging technology".
For example, Google DeepMind (uses deep learning) "can quickly interpret eye scans from routine clinical practice with unprecedented accuracy. It can correctly recommend how patients should be referred for treatment for over 50 sight-threatening eye diseases as accurately as world-leading expert doctors" https://deepmind.com/blog/moorfields-major-milestone/ - see their paper at https://www.nature.com/articles/s41591-018-0107-6
Additional examples are available in the following G+ Collection of mine on the subject of 'Cognitive Computing & AI in Health/care (IBM Watson Health, Google DeepMind, Machine Learning, etc.)' at https://plus.google.com/collection/40E-LE
Perhaps one of the most interesting applications is in the design of "dynamic biomarkers". That is to say, biomarkers whose meaning is extracted from its variation and relations of variation at certain moments instead of its absolute value.