**Carla M. A. Pinto 1,2,\*,†, Ana R. M. Carvalho 3,†, Dumitru Baleanu 4,† and Hari M. Srivastava 5,6,†**


Received: 17 April 2019; Accepted: 4 June 2019; Published: 5 June 2019

**Abstract:** We propose a fractional order model to study the efficacy of the Post-Exposure Prophylaxis (PEP) in human immunodeficiency virus (HIV) within-host dynamics, in the presence of the HIV latent reservoir. Latent reservoirs harbor infected cells that contain a transcriptionally silent but reactivatable provirus. The latter constitutes a major difficulty to the eradication of HIV in infected patients. PEP is used as a way to prevent HIV infection after a recent possible exposure to HIV. It consists of the in-take of antiretroviral drugs for, usually, 28 days. In this study, we focus on the dosage and dosage intervals of antiretroviral therapy (ART) during PEP and in the role of the latent reservoir in HIV infected patients. We thus simulate the model for immunologically important parameters concerning the drugs and the fraction of latently infected cells. The results may add important information to clinical practice of HIV infected patients.

**Keywords:** Post-Exposure Prophylaxis; latent reservoir; HIV infection; fractional order model
