We investigate the phenomenon of HIV eradication at the early stage of the infection and evaluate the chance of the eradication with a mathematical model. We employ an extracellular deterministic model of the HIV infection dynamics and modify the model to include the pharmacokinetics and pharmacodynamics of antiretroviral HIV drugs. In addition we consider clinical experiments for the prevention of HIV infection using pre-exposure chemoprophylaxis treatment. Exploiting the mathematical model we implement the experiment numerically. The study in this paper is supported by the clinical results and provides a theoretical explanation for the results. The result suggests that the protocol of the experiment eradicates the virus in HIV infected patients.