**6. Conclusions**

We propose a model to study the effect of PEP and of the latent reservoir in the dynamics of HIV infection. We find that specific dosages and intervals are extremely important to control the infection. Moreover, we find that the latent reservoir may influence the dynamics of HIV, though slightly. This is understandable from a clinical point of view since the effect of the latent reservoir takes time to be felt and PEP is considered only in the first 28 days after exposure. After that, the person must be evaluated clinically to assess the adequacy of the treatment. The order of the fractional derivative, *α*, seems to help control the infection in the presence of PEP and increases the severity of infection when there is no PEP. We observe a somewhat 'synergistic' relation between PEP and *α*. The FO derivative may also help to distinguish other traits (age, immune system response, genetic profile), and this may help to devise better therapeutic regimens, that could improve patients' quality of life, either by diminishing the burden of the therapy or increasing the life span. Moreover, since HIV anti-retroviral therapy (ART) is extremely expensive, an 'optimal' (in the sense of more adjusted to each patient) therapy could also imply a reduction in the economic burden of HIV, especially in poor countries, such as the ones included in sub-Saharan Africa. Future work will focus on deepening these and other issues arising from the model.

**Author Contributions:** All authors contributed equally to the work reported.

**Acknowledgments:** The authors were partially funded by the European Regional Development Fund through the program COMPETE and by the Portuguese Government through the FCT - Fundação para a Ciência e a Tecnologia under the project PEst-C/MAT/UI0144/2013. The research of AC was partially supported by an FCT grant with reference SFRH/BD/96816/2013.

**Conflicts of Interest:** The authors declare no conflict of interest.
