In most people infected with human immunodeficiency virus (HIV), their immune system cannot control HIV infection. They need drugs called combination antiretroviral therapy (cART) to control the HIV. When people stop cART treatment, their immune system cannot control the infection again. They can also become resistant to cART and have lasting side effects. Researchers want to test if the drug vedolizumab is effective at controlling HIV infection without the need for cART.