When we apply the differential privacy on medical data to protect the personal data of the patients, how the doctors can access the original data to analyze them and to intervene in real-time. In other words, the added noise to disturb the data, can be eliminated?
I'm not an expert in differential privacy, but I remember that the main idea of these techniques is not to eliminate the noise to analyse individual data, but to analyse directly the noisy data (that's why there is a tradoff privacy/relevancy of the data when you choose the value of the noise).
Differential privacy does not help to prevent disclosure of individual records when the user—the doctor, in this case—needs access to the individual records themselves.
Differential privacy is a property of a system for aggregating a collection of records into statistical queries on a data set so that the inclusion or exclusion of an individual record can't change the answers to the statistical queries much. That way, the answers to the statistical queries—which might be published in a medical journal, or used to study trends—can't reveal much about individual patients.
Differential privacy is not intended for uses where access to individual records is necessary. For example a doctor needs access to her patient's medical records, and a police officer need access to the criminal record of someone they have arrested. In these cases, the privacy protection is that only trusted users (doctors, police officers, etc.) have access to the relevant information and they only access it as needed.
As Squeamish Ossifrage's answer explains, differential privacy is intended for statistical uses where access to individual records is not necessary. Since the results of a statistical analysis may be made public (e.g. in a published medical study, which can be accessed by untrusted parties), we need a differentially private method to provide rigorous privacy protection.