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The Centers for Disease Control website provides vaccination advice.
Check the vaccines and medicines list and visit your doctor (ideally, 4-6 weeks) before your trip to get vaccines or medicines you may need.
For Yellow fever it states:
There is no risk of yellow fever in South Africa. The government of South Africa requires proof of yellow fever vaccination only if you are arriving from a country with risk of yellow fever
India is not on the list.
The recommended vaccines depend on which you already have, what country you live in, and your anticipated activities. For example, a rabies vaccination may be recommended if you are camping, but not if you are attending a conference.
By the way, your doctor is probably going to be the best person to give you advice. He or she should be familiar with the vaccination requirements of your destination country, or at least be able to find them readily, as well as the applicability to you and your situation.