Добавил Id во все вьюхи в логике

Medical/MedicalBusinessLogic/BusinessLogics/DoctorLogic.cs

@@ -51,6 +51,7 @@ namespace MedicalBusinessLogic.BusinessLogics
         protected override DoctorViewModel GetViewModel(Doctor model)
         {
             var doctorViewModel = new DoctorViewModel {
+                Id = model.Id,
                 Name = model.Name,
                 Surname = model.Surname,
                 Patronymic = model.Patronymic ?? string.Empty,

Medical/MedicalBusinessLogic/BusinessLogics/PatientLogic.cs

@@ -45,6 +45,7 @@ namespace MedicalBusinessLogic.BusinessLogics
         {
             return new PatientViewModel
             {
+                Id = model.Id,
                 Name = model.Name,
                 Surname = model.Surname,
                 Patronymic = model.Patronymic ?? string.Empty,

Medical/MedicalBusinessLogic/BusinessLogics/SpecializationLogic.cs

@@ -44,6 +44,7 @@ namespace MedicalBusinessLogic.BusinessLogics
         protected override SpecializationViewModel GetViewModel(Specialization model)
         {
             return new SpecializationViewModel {
+                Id = model.Id,
                 Name = model.Name,
                 IsPediatric = model.IsPediatric,
                 IsTherapeutic = model.IsTherapeutic

Medical/MedicalBusinessLogic/BusinessLogics/VisitLogic.cs

@@ -65,7 +65,8 @@ namespace MedicalBusinessLogic.BusinessLogics
 
         protected override VisitViewModel GetViewModel(Visit model)
         {
-            var visitViewModel = new VisitViewModel { 
+            var visitViewModel = new VisitViewModel {
+                Id = model.Id,
                 PatientId = model.PatientId,
                 DoctorId = model.DoctorId,
                 DiagnoseId = model.DiagnoseId,