In the present work a study of the dynamics of insulin-glucose is performed for both a healthy person and a patient who has already contracted diabetes; The different types of diabetes are indicated as well as the symptoms that characterize it. The models that simulate the insulin-glucose dynamics for a healthy person are presented, and later the corresponding changes are made to simulate the process in a diabetic; The system is simplified in correspondence with the critical case considered, if a qualitative study of the system of equations is made and conclusions are made regarding the future behavior of the disease.