**1. Introduction**

The human immunodeficiency virus (HIV) is a retrovirus, which impairs the host immune system, by destroying preferably the CD4<sup>+</sup> T cells. These cells are essential to guarantee immune protection. They do so by helping B cells produce antibodies, inducing macrophages to develop enhanced microbicidal activity, recruiting neutrophils, eosinophils, and basophils to inflammation and infection sites, and, by producing cytokines and chemokines. A number of CD4<sup>+</sup> T cells below a given threshold is a synonym of immunodeficiency. The organism is thus vulnerable to a broad set of infections, cancers and other diseases.

HIV occurs in two types: HIV-1 and HIV-2, and is transmitted by the exchange of HIV-infected body fluids, such as blood, semen, and genital secretions. It may also be transmitted from an HIV-infected pregnant woman to her child, during pregnancy, birth, or breastfeeding [1].

HIV is a defying global health threat, responsible for more than 36.7 million infected people worldwide, and more than 35 million deaths, so far. In 2016, the number of deceased from HIV-related causes was estimated at one million. Figures are even more striking since, globally, 1.8 million people become newly infected each year. Access to antiretroviral therapy is crucial to control the virus and to reduce the risk of transmission, providing HIV infected individuals and those at risk, more healthy, long and productive lives. In 2016, nearly half of the adults and children living with HIV had access to treatment. Effective treatment reduces the risk of HIV transmission to non-infected sexual partners by 96% [2]. Other forms of HIV prevention are the Pre-Exposure Prophylaxis (PrEP) and the Post-Exposure Prophylaxis (PEP).

PrEP is the daily in-take of ART to prevent HIV infection in uninfected people. The usual combination of the two HIV drugs, tenofovir and emtricitabine, sold under the name of Truvada, is approved for daily use as PrEP. PrEP is shown to be highly effective for HIV prevention, when taken consistently. WHO recommends PrEP as one of the prevention options, for people at substantial risk of HIV infection (namely injecting drug users, men who have sex with men, and high-risk heterosexual couples), and for HIV-negative women who are pregnant or breastfeeding [2].

PEP consists of the intake of ART, after possible exposure to HIV. It includes counseling, first aid care, HIV testing, and administration of a 28-day course of ART with follow-up care. It is intended to prevent HIV spread in the human body, protecting against being re-exposed to HIV and reducing the chances of HIV transmission [3]. PEP was initially intended for healthcare workers, who had been accidentally exposed to HIV-infected body fluids, through injury with a contaminated syringe, etc. Nowadays, WHO recommends PEP for both health-worker and non-health-workers, for adults and children [2]. PEP should be started immediately after exposure and at most 72 hours after, to enhance the rate of success, since it is not 100% effective [3].

Latent reservoirs consist of a small proportion of resting CD4<sup>+</sup> T cells, containing integrated proviral DNA [4–6]. Latent reservoirs are established during the acute phase of HIV infection. These reservoirs may hide out for years in many tissues in the body, namely lymph nodes, seminal fluid, and cerebral spinal fluid. Latent reservoirs can, however, wake up, and release old viral variants in the blood. The mechanism behind this activation is summarized as follows. Proviral genomes are integrated in resting memory CD4<sup>+</sup> T cells. Due to the quiescent state of these latent cells, these genomes are not transcribed into mRNA (messenger ribonucleic acid) and translated in protein to become active virus. Nevertheless, when cell activation occurs, then transcription and translation may recommence [7]. This affects the viral dynamics of untreated patients, promoting viral load rebounds. ART can suppress HIV load levels to undetectable values, however, it cannot eliminate the latent reservoir. This is the main challenge to HIV cure.

Considerable research has been found in the literature to describe the effects of HIV prevention strategies. In 2009, Lou et al. [8] study drug dynamics, drug dosages, and therapy strategies in an impulsive model for the dynamics of HIV in the presence of PEP. Authors conclude that the best choice for an infected individual is a safe dose of medication during PEP. Moreover, the side effects of ART should also be taken into consideration in choosing the appropriate therapy. Conway et al. [9] present a stochastic model for the dynamics of HIV, immediately after exposure, and apply drug prophylaxis to understand how it reduces the risk of infection. The authors predict that a two-week PEP regimen may be as effective as the recommended four-week treatment protocol. In 2014, Kim et al. [10] study a model for HIV infection in men who have sex with men (MSM) in South Korea. They simulate the effects of early ART, early diagnosis, PrEP, and combination interventions, on the incidence and prevalence of HIV infection. The authors conclude that PrEP and early diagnosis would be effective ways in reducing HIV incidence in MSM. In 2017, Pinto et al. [11], evaluate the impact of PrEP and screening in the dynamics of HIV in infected patients. The proposed model incorporates condom use, the number of sexual partners, and treatment for HIV. The basic reproduction number is extremely impacted by the efficacy of the screening, pointing to explicit campaigns highlighting screening. The results from the model are fitted to data on the cumulative HIV and AIDS (acquired immunodeficiency syndrome) cases in Portugal.
